Andreas Krug
We compute a formula for the discriminant of tautological bundles on symmetric powers of a complex smooth projective curve. It follows that the Bogomolov inequality does not give a new restriction to stability of these tautological bundles. It only rules out tautological bundles which are already known to have the structure sheaf as a destabilising subbundle.
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We give a criterion for extending a generically semisimple (not necessarily conformal) Frobenius manifold locally near a smooth point of the discriminant to a cohomological field theory. As an application, we show that a large set of tautological relations related to the Givental--Teleman classification for any generically semisimple cohomological field theories follow from Pixton's generalized Faber--Zagier relations.
Stability of tautological vector bundles on Hilbert squares of surfaces
证明了曲面的Hilbert平方上秩为2的重言式丛的稳定性（在弱正性条件下），并计算了它们的Chern类。
We compute the Euler characteristics of tautological vector bundles and their exterior powers over the Quot schemes of curves. We give closed-form expressions over punctual Quot schemes in all genera. For higher rank quotients of a trivial vector bundle, we obtain answers in genus zero. We also study the Euler characteristics of the symmetric powers of the tautological bundles, for rank zero quotients.
Extension Groups of Tautological Bundles on Punctual Quot Schemes of Curves
本文证明了曲线上点态 Quot 概形上重言丛的上同调与扩张群公式，并由此推出重言丛决定原始向量丛的同构类，同时给出沿 Quot--Chow 态射推前的消失结果。
On projective space bundle with nef normalized tautological divisor
本文研究了相对反标准线丛为nef的射影空间丛的结构。作为应用，我们得到了有限余覆盖下的阿贝尔簇的一个刻画。
We study the images of tautological bundles on Hilbert schemes of points on surfaces and their wedge powers under the derived McKay correspondence. The main observation of the paper is that using a derived equivalence differing slightly from the standard one considerably simplifies both the results and their proofs. As an application, we obtain shorter proofs for known results as well as new formulae for homological invariants of tautological sheaves. In particular, we compute the extension groups between wedge powers of tautological bundles associated to line bundles on the surface.
We calculate the Euler characteristic of associated vector bundles over the moduli spaces of stable parabolic bundles on smooth curves. Our method is based on a wall-crossing technique from Geometric Invariant Theory, certain iterated residue calculus and the tautological Hecke correspondence. Our work was motivated by the results of Teleman and Woodward on the index of K-theory classes on moduli stacks.
Moduli spaces of generalised tautological bundles on Hilbert schemes
本文在代数曲面点的 Hilbert 概形上构造了由模空间连通分支参数化的新稳定向量丛，推广了先前关于重言丛及 O'Grady 的近期研究。
Tensor products of tautological bundles under the Bridgeland-King-Reid-Haiman equivalence
在Bridgeland-King-Reid-Haiman等价下，给出重言丛的张量积在曲面上点的Hilbert概型上的象.在此基础上，得到了这类丛的上同调不变量的一些新公式。特别地，我们给出了两点Hilbert格式上任意张量积的欧拉示性数的计算公式，以及一般三重张量积的计算公式。
We prove that, if $C$ is a smooth projective curve over the complex numbers, and $E$ is a stable vector bundle on $C$ whose slope does not lie in the interval $[-1,n-1]$, then the associated tautological bundle $E^{[n]}$ on the symmetric product $C^{(n)}$ is again stable. Also, if $E$ is semi-stable and its slope does not lie in the interval $(-1,n-1)$, then $E^{[n]}$ is semi-stable.
Geometry and stability of tautological bundles on Hilbert schemes of points
本文的目的是探讨光滑曲面上点的Hilbert格式上重言式向量丛的几何性质并建立其斜率稳定性。通过建立一般稳定性，我们完成了Schlickewei和Wandel的一系列结果，他们证明了这些向量丛对于K3或交换曲面上的2点或3点Hilbert格式在Picard群限制下的斜率稳定性。在探索几何中，我们证明了平滑曲线上的每一个充分正的半稳定向量丛都是由于射影平面上的点的Hilbert方案上的重言式向量丛的限制而产生的。此外，我们还证明了切丛的重言丛自然同构于与因子相切的由非约化子概型组成的向量场层。
In this paper, our aim is to find the relations amongst the cohomology classes of Brill-Noether subvarieties of the moduli space of semistable bundles over an elliptic curve. We obtain results similar to the Poincaré relations on a Jacobian variety.
Tautological module and intersection theory on Hilbert schemes of nodal curves
研究了任意维基上一类光滑或平滑曲线族的相对Hilbert格式的相交理论。我们引入了一个添加剂组称为“判别模块”，产生的对角线轨迹，节点滚动，和扭曲，并确定行动的判别或大对角因子对这个组的交叉。我们表明，这足以确定任意多项式的陈类，特别是陈数，重言式向量丛的希尔伯特计划，这是密切相关的枚举几何。最新的版本包括一些新的显式计算和参考的计算机程序，由于G。刘实现了我们的交集演算。
On the cohomology of tautological bundles over Quot schemes of curves
研究曲线商上塔利奥格利 bundles 的外幂和对称幂的上同调消失问题，通过构造具有消失上同调的解析，描述其全局截面空间。
We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each K-trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the K3 case, we extend recent constructions and results of Bini, Boissière and Flamini from the Hilbert scheme of 2 and 3 points to an arbitrary number of points. Among the K-trivial surfaces, the case of Enriques surfaces is the most involved. Our techniques apply to other smooth projective surfaces, including blowups of K3s and minimal surfaces of general type,…
We propose a conjecture on the generating series of Chern numbers of tautological bundles on Hilbert schemes of points on curves and establish the rank 1 and rank -1 case of this conjecture. Thus we compute explicitly the generating series of integrals of the Segre classes of tautological bundles of line bundles on curves, which has a similar structure as Lehn's conjecture for surfaces.
We first give an alternative proof, based on a simple geometric argument, of a result of Marian, Oprea and Pandharipande on top Segre classes of the tautological bundles on Hilbert schemes of $K3$ surfaces equipped with a line bundle. We then turn to the blow-up of $K3$ surface at one point and establish vanishing results for the corresponding top Segre classes in a certain range. This determines, at least theoretically, all top Segre classes of tautological bundles for any pair $(Σ,H),\,H\in {\rm Pic}\,Σ$.
Tautological ring of the moduli space of generalised parabolic line bundles on a curve
本文考虑复结点射影曲线的紧化雅可比矩阵的正规化上的重言式环，它包含扩张的Brill-Noether代数类.这种代数等价下代数类的最小$\Q$ -子代数，在乘法映射、Pontrayagin积和傅里叶变换所诱导的映射的扩张下是稳定的，是由正规化曲线的Jacobian的Brill-Noether类和某些自然类的拉回所产生的.
Given a vector bundle $E$ on a smooth projective curve or surface $X$ carrying the structure of a $V$-twisted Hitchin pair for some vector bundle $V$, we observe that the associated tautological bundle $E^{[n]}$ on the punctual Hilbert scheme of points $X^{[n]}$ has an induced structure of a $((V^\vee)^{[n]})^\vee$-twisted Hitchin pair, where $(V^\vee)^{[n]}$ is a vector bundle on $X^{[n]}$ constructed using the dual $V^\vee$ of $V$. In particular, a Higgs bundle on $X$ induces a logarithmic Higgs bundle on the Hilbert scheme $X^{[n]}$. We then show that the known results on stability of tauto…
Chern Classes of Tautological Sheaves on Hilbert Schemes
我们给出了一个算法描述的行动的陈类重言丛上的Hilbert计划的上同调的点表面内的Nakajima的振子代数的框架。这导致识别的上同调环的希尔伯特计划的仿射平面与一个环的微分算子的Fock空间。最后计算了Hilb^n上直到n=7的线丛的重言式丛的顶Segre类，并给出了生成级数的一个猜想。
Parabolic k-ample bundles
我们构造了抛物向量丛和其上重言线丛的射影化，证明了抛物向量丛是充分的当且仅当重言线丛是充分的.这使我们能够推广的概念，一个k-样本丛，介绍了Sommese，抛物丛的背景下。定义抛物向量丛$E_*$是k-样本的，如果重言式线丛${\mathcal O}_{{\mathbb P}(E_*)}(1)$是$k$ -样本的.建立了抛物k-样本丛的一些性质。
Stability of tautological bundles on the Hilbert scheme of two points on a surface
设（X，H）是满足H^1（X，O_X）=0的极化光滑射影曲面，F是X上的秩1无挠层或秩2 μ H-稳定向量丛.假设c_1（F）/=0。本文证明了Hilbert平方X^{[2]}上与F相关联的秩2和秩4重言式层F^{[2]}对某个极化是μ-稳定的。
We provide a spectral sequence computing the extension groups of tautological bundles on symmetric products of curves. One main consequence is that, if $E\neq \mathcal O_X$ is simple, then the natural map $\operatorname*{Ext}^1(E,E)\to \operatorname*{Ext}^1(E^{[n]},E^{[n]})$ is injective for every $n$. Along with previous results, this implies that $E\mapsto E^{[n]}$ defines an embedding of the moduli space of stable bundles of slope $μ\notin[-1,n-1]$ on the curve $X$ into the moduli space of stable bundles on the symmetric product $X^{(n)}$. The image of this embedding is, in most cases, cont…
Let U be the tautological subbundle on the Grassmannian $\mathrm{Gr}(k, n)$. There is a natural morphism $\mathrm{Tot}(U) \to \mathbb{A}^n$. Using it, we give a semiorthogonal decomposition for the bounded derived category $D^b_{\mathrm{coh}}(\mathrm{Tot}(U))$ into several exceptional objects and several copies of $D^b_{\mathrm{coh}}(\mathbb{A}^n)$. We also prove a global version of this result: given a vector bundle $E$ with a regular section $s$, consider a subvariety of the relative Grassmannian $\mathrm{Gr}(k, E)$ of those subspaces which contain the value of $s$. The derived category of t…
A construction of Chern classes of parabolic vector bundles
给定一个抛物型向量丛，我们构造了它的一个射影化重言式线丛。这些都类似于通常的向量丛的射影化和重言式线丛。利用这些，我们给出了一个建设的抛物陈类。
Derived categories of Quot schemes on smooth curves and tautological bundles
本文研究了光滑曲线上的有限长度商丛的导出范畴，定义了移位量子环状群作用，并通过分解计算塔利奥尼亚丛的上同调。
Extension groups of tautological sheaves on Hilbert schemes
给出了光滑拟射影曲面上点的Hilbert概型上重言式层之间以及更一般的被行列式线丛扭曲的重言式对象之间的扩张群的公式。我们用L来做这个。Scala关于Bridgeland-King-Reid等价下重言层象的结果。我们还计算米田产品的这些公式。
Cohomologies of tautological bundles of matroids
本文计算了拟阵实现的重言层丛的外幂与对称幂的上同调，证明其仅依赖于拟阵本身，并由此推出超平面排列补集绝妙紧化的对数典范丛高阶上同调消失。
We study general symmetric powers $S^k L^{[n]}$ of a tautological bundle $L^{[n]}$ on the Hilbert scheme $X^{[n]}$ of $n$ points over a smooth quasi-projective surface $X$, associated to a line bundle $L$ on $X$. Let $V_L$ be the $\mathfrak{S}_n$-vector bundle on $X^n$ defined as the exterior direct sum $L \boxplus \cdots \boxplus L$. We prove that the Bridgeland-King-Reid transform $\mathbfΦ(S^k L^{[n]})$ of symmetric powers $S^k L^{[n]}$ is quasi isomorphic to the last term of a finite decreasing filtration on the natural vector bundle $S^k V_L$, defined by kernels of operators $D^l_L$, whic…
Let S be a nonsingular projective surface. Each vector bundle V on S of rank s induces a tautological vector bundle over the Hilbert scheme of n points of S. When s=1, the top Segre classes of the tautological bundles are given by a recently proven formula conjectured in 1999 by M. Lehn. We calculate here the Segre classes of tautological bundles for all ranks s over all K-trivial surfaces. Furthermore, in rank s=2, the Segre integrals are determined for all surfaces, thus establishing a full analogue of Lehn's formula. We also give conjectural formulas for certain series of Verlinde Euler cha…
Discriminant divisors for conic bundles
本文研究一般光滑圆锥丛判别子的基础性质，并将其判别子与相对典范类平方的公式推广至任意特征。
By analyzing degeneracy loci over projectivized vector bundles, we recompute the degree of the discriminant locus of a vector bundle and provide a new proof of the Bogomolov instability theorem.
Recently, Oh and Thomas constructed algebraic virtual cycles for moduli spaces of sheaves on Calabi-Yau 4-folds. The purpose of this paper is to provide a virtual pullback formula between these Oh-Thomas virtual cycles. We find a natural compatibility condition between 3-term symmetric obstruction theories that induces a virtual pullback formula. There are two types of applications. Firstly, we introduce a Lefschetz principle in Donaldson-Thomas theory, which relates the tautological DT4 invariants of a Calabi-Yau 4-fold with the DT3 invariants of its divisor. As corollaries, we prove the Cao-…
Strata of $k$-differentials on smooth curves parameterize sections of the $k$-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the $κ$ and $ψ$ classes of moduli spaces of pointed smooth curves along with the tautological class $η$ of the Hodge bundle. We show that if there is no pole of order $k$, then the tautological ring is generated by $η$ only, and otherwise it is generated by the $ψ$ classes corresponding to the poles of order $k$.
Tautological algebra of the moduli stack of semistable bundles of rank 2 on a general curve
研究一般曲线上的秩2稳定丛模堆栈的拟代数结构，揭示其由除子类生成的性质，扩展经典Porteous公式的应用。
For $G$ a finite subgroup of ${\rm SL}(3,{\mathbb C})$ acting freely on ${\mathbb C}^3{\setminus} \{0\}$ a crepant resolution of the Calabi-Yau orbifold ${\mathbb C}^3\!/G$ always exists and has the geometry of an ALE non-compact manifold. We show that the tautological bundles on these crepant resolutions admit rigid Hermitian-Yang-Mills connections. For this we use analytical information extracted from the derived category McKay correspondence of Bridgeland, King, and Reid [J. Amer. Math. Soc. 14 (2001), 535-554]. As a consequence we rederive multiplicative cohomological identities on the cre…
We give an algebraic proof valid in arbitrary characteristic for the known equivalence between (strongly) slope semistable vector bundles with vanishing discriminant and vanishing determinant and numerically flat bundles. We also address a related question of Misra.
Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles
设$X$为光滑拟射影代数曲面，$L$为$X$上的线丛.设$X^{[n]}$为$X$上$n$点的Hilbert概型，$L^{[n]}$为自然地与$X$上的线丛$L$相关联的$X^{[n]}$上的重言式丛。我们根据$\B{D}^b_{\perm_n}(X^n)$中$\perm_n$ -等变层的复$\comp{\mc{C}}_L$，显式地计算了Bridgeland-King-Reid等价$\bkrh : \B{D}^b(X^{[n]}) \ra \B{D}^b_{\perm_n}(X^n)$的重言丛$L^{[n]}$的象$\bkrh(L^{[n]})$。此外，我们给出了一个表征的图像$\bkrh(L^{[n]} \tens ... \tens L^{[n]})$的超衍生光谱序列$E^{p,q}_1$相关的衍生$k$倍张量功率的复杂$\comp{\mc{C}}_L$。研究这个谱序列的$\perm_n$ -不变量，可以得到希尔伯特-周态射重言丛的双张量幂和广义$k$ -折叠外幂的直接图像，在这两种情况下提供Danila-Brion型公式。这就很容易计算出$X^{[n]}$的上同调，其值在$L^{[n]} \tens L^{[n]}$和$Λ^k L^{[n]}$中。
On the unirationality of conic bundles with discriminant of degree eight
本文研究了判别次数为八的锥面的不可理化性，通过构造有理多截面和变形理论分析，揭示了其在不同域上的不可理化性质。
Sur la cohomologie d'un fibre tautologique sur le schema de Hilbert d'une surface
本文计算了光滑射影曲面X的长为n的子概型的点希尔伯特概型H上的重言式丛张量行列式丛的上同调空间。本文证明了对X上的可逆向量丛L和A，以及X的典范丛，如果$w^{-1}\otimes L$，$w^{-1}\otimes A$和A是充分向量丛，则L张量所对应的重言式丛和A所对应的行列式丛在H上的高上同调空间为零，并且整体瓣空间是用$H^0(A)$和$H^0(L\otimes A)$计算的.这个结果是由计算射影平面上秩为2的半稳定层的模空间上的行列式丛的整体瓣空间所得到的，支持了射影平面上的Le Potier的Strange对偶猜想.
Dimer models and crepant resolutions
研究了在稳定性参数变化的条件下，重言式丛在具有关系的箭图表示的模空间上的变化。证明了重言式丛对某个稳定性参数导出等价，则对任何一般稳定性参数导出等价，且任何射影收缩分解都可以作为某个稳定性参数的模空间得到.该结果用于0905.0059，以证明阿贝尔麦凯对应关系，而不使用math/9908027的结果。
The McKay Correspondence for Dihedral Groups: The Moduli Space and the Tautological Bundles
本文证实了关于二面体群（作为复反射群）的McKay对应猜想，即解消与模空间同构当且仅当被极大解消支配，并推广了McKay对应。
Incidence varieties in the projectivized $k$-th Hodge bundle over curves with rational tails
本文研究了带标点光滑代数曲线模空间上射影化 $k$ 次 Hodge 丛中的关联轨迹，计算了其在有理尾曲线模空间上闭包的示性类，并以此获得了有理尾曲线模示性环中某些关系的显式表达式。
Cycles Representing The Top Chern Class of the Hodge Bundle on the Moduli Space of Abelian Varieties
我们将著名的亏格1的公式$12 λ=δ$推广到更高的亏格。我们还计算类的某些阶层的佐竹紧化的重言式环的下推的元素。
We study real double covers of $\mathbb P^1\times\mathbb P^2$ branched over a $(2,2)$-divisor, which have the structure of a conic bundle threefold with smooth quartic discriminant curve via the second projection. In each isotopy class of smooth plane quartics, we construct examples where the total space of the conic bundle is rational. For five of the six isotopy classes we construct $\mathbb C$-rational examples that have obstructions to rationality over $\mathbb R$, and for the sixth class, we show that the models we consider are all rational. Moreover, for three of the five classes with ir…
A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$
本文研究 $\mathbb{P}^1$ 上 Quot 概形中重言丛的上同调，建立了相应的 Borel–Weil–Bott 定理，并由此证明了 Marian、Oprea 和 Sam 关于重言丛外幂与对称幂的猜想。
We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section over the second Voronoi compactification of the moduli of principally polarized abelian varieties also can not be expressed in terms of classes of degree 1 and 2. Along the way, we establish new cases of Pixton's conjecture for tautological relations. In the log Chow ring of the moduli space of curves, however, we prove that the top Chern class of the Hodge b…
We introduce a new family of tautological relations of the moduli space of stable curves of genus $g$. These relations are obtained by computing the Poincaré-dual class of empty loci in the Hodge bundle. We use these relations to obtain a new expression for the Chern classes of the Hodge bundle. We prove that the $(g-i)$th class can be expressed as a linear combination of tautological classes involving only stable graphs with at most $i$ loops. In particular the top Chern class may be expressed with trees. This property was expected as a consequence of the DR/DZ equivalence conjecture by Burya…
Vanishing theorems on wonderful varieties
本文研究了奇妙簇上重言丛的消没定理，证明了Brieskorn结果的类似物及Orlik--Solomon代数的比较定理，扩展了Borel--Weil--Bott型消没定理，并将White基猜想的弱版本归约为上同调消没问题。
Sur la cohomologie de la puissance symetrique du fibre tautologique sur le schema de Hilbert ponctuel d'une surface
本文计算了复光滑射影曲面上点希尔伯特格式上重言丛张量行列式丛的对称幂的上同调空间。
Geometry and intersection theory on Hilbert schemes of families of nodal curves
我们研究了一族节点（或光滑）曲线的相对Hilbert方案，在任意维的基上，通过它的（双有理）循环映射，到相对对称积。我们证明了循环图是判别轨迹的爆破，它由具有重点的循环组成。我们计算了Hilbert格式中的一些自然循环的爆破或“判别”极化的作用，包括广义对角线和循环，称为“节点涡卷”，支持在奇点上的参数化格式.本文导出了重言式向量丛的陈类的交演算，这类向量丛与枚举几何密切相关。
The Chow ring of the moduli space of curves of genus 6
通过证明所有Chow类都是重言式，确定了M_6的Chow环（具有Q系数）.特别地，所有代数上同调是重言式的，并且从Chow到上同调的自然映射是内射的。为了证明这些方法的实用性，我们也给出了下亏格曲线的模空间的Chow群的快速推导。亏格6的情形依赖于特别漂亮的Brill-Noether理论，特别是秩5的向量丛“相对化”了Mukai的一个著名构造的一个婴儿情形，我们将其解释为切除典范曲线的秩6的二次曲面的向量丛的一个子丛。
Computations of Bott-Chern classes on P(E)
计算了复流形上全纯厄米向量丛（E，h）的超平面簇P（E）的相对切丛的度量欧拉序列的Bott-Chern类.给出了算术向量丛的算术特征类的构造和P（E）关于重言式商丛O_E（1）的高度的计算.
Lifting vector bundles to Witt vector bundles
本文研究将概形上的向量丛提升为Witt向量丛的问题，给出线丛和射影丛情形下的正结果，推广形变理论至约化概形，并证明Grassmannian的平凡向量丛在特定条件下不可提升。
The special linear version of the projective bundle theorem
一个特殊的线性Grassmann簇SGr（k，n）是Gr（k，n）上重言式向量丛的行列式的零截面的补.对于具有特殊线性方向和可逆稳定Hopf映射η的可表示环上同调理论A（-），包括Witt群和MSL[η^{-1}]，我们有A（SGr（2，2n+1））=A（pt）[e]/（e^{2n}），A（SGr（2，2n））是A（pt）上的截断二元多项式代数.建立了这类理论的分裂原理。利用对特殊线性Grassmann簇的计算，我们计算了重言丛的某些特征类中齐次幂级数的A（BSL_n）.
Discriminant loci of ample and spanned line bundles
设$(X,L,V)$是一个三元组，其中$X$是一个不可约的光滑复射影簇，$L$是$X$上的一个充裕的张成线丛，$V\subseteq H^0(X,L)$张成$L$ .判别轨迹$\Cal D(X,V) \subset |V|$是$|V|$的奇异元素的代数子集。本文研究了$\Cal D(X,V)$的分支与$(X,V)$的跳集的关系，推广了经典的对偶定理.我们还处理的程度的判别式（$(X,L,V)$的余度）给出了一些界限，它和分类的曲线和曲面的余度2和3。我们排除了余度为1的可能性。提供了重要的例子。
Hausel introduced a commutative algebra -- the multiplicity algebra -- associated to a fixed point of the C^*-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the discriminant of this family, providing a new viewpoint on the moduli space of stable bundles. The discriminant in our examples demonstrates that as the bundle varies, we obtain a continuous variation in …
Higher discriminants of vector bundles and Schur functors
本文证明了局部自由层对数 Chern 特征的闭式公式，利用表示论与 Casimir 元素，并应用于构造超 Kähler 流形上的斜率多重稳定模丛。
We prove an explicit formula for the total Chern character of the Verlinde bundle over the moduli space of pointed stable curves in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman's classification of semisimple CohFTs, there exists an element of Givental's group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the moduli space of nonsingular curves and the proje…
We define and study the quantum equivariant $K$-theory of cotangent bundles over Grassmannians. For every tautological bundle in the $K$-theory we define its one-parametric deformation, referred to as quantum tautological bundle. We prove that the spectrum of operators of quantum multiplication by these quantum classes is governed by the Bethe ansatz equations for the inhomogeneous $XXZ$ spin chain. In addition, we prove that each such operator corresponds to the universal elements of quantum group $\mathcal{U}_{\hbar}(\widehat{\mathfrak{sl}}_2)$. In particular, we identify the Baxter operator…
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