首页/论文/2003.07297

arXiv 2003.072972020-03math.QAmath.AG

Real Springer fibers and odd arc algebras

Jens Niklas Eberhardt, Grégoire Naisse, Arik Wilbert

备注：: v3, 42 pages, minor corrections, revised version to appear in J. Lond. Math Soc
DOI：: 10.1112/jlms.12413

英文摘要：

We give a topological description of the two-row Springer fiber over the real numbers. We show its cohomology ring coincides with the oddification of the cohomology ring of the complex Springer fiber introduced by Lauda-Russell. We also realize Ozsváth-Rasmussen-Szabó odd TQFT from pullbacks and exceptional pushforwards along inclusion and projection maps between hypertori. Using these results, we construct the odd arc algebra as a convolution algebra over components of the real Springer fiber, giving an odd analogue of a construction of Stroppel-Webster.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

编织与双列斯宾纳纤维的光滑成分

Webs and smooth components of two column Springer fibers

University of Waterloo（滑铁卢大学）

本文通过编织与双列矩形斯宾纳纤维的对应关系，揭示了光滑成分的几何结构，并证明了其Poincaré多项式在编织的二面体作用下保持不变。

2026-09-28math.AGmath.COmath.QA

Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory

We explain an elementary topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two Jordan blocks. The Weyl group and component group actions admit a diagrammatic description in terms of cup diagrams which appear in the definition of arc algebras of types B and D. We determine the decomposition of the representations into irreducibles and relate our construction to classical Springer theory. As an application we obtain presentations of the cohomology rings of all two-block Springer fi…

2018-08-30math.GTmath.QAmath.RT

On the homology of exotic Springer fibers

The author decided to withdraw this paper by 1) an error in Lemma 5.11 (and 5.12) which requires some justification; 2) the main result of this paper suffers overlap with arXiv:1203.5254; 3) the author decided to split arXiv:1203.5254 into two pieces, and the main application of this paper is transferred to one of them (in order to keep strength of the applications presented in each paper); and 4) thus a "newer version" of this paper would have different story and substantially different contents, which he feels a different paper.

2012-07-19math.AGmath.QAmath.RT

Exotic Springer fibers for orbits corresponding to one-row bipartitions

We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components and their intersections as well as the construction of an explicit affine paving. Moreover, we compute the ring structure of cohomology by constructing a CW-complex homotopy equivalent to the exotic Springer fiber. This homotopy equivalent space admits an action of the type C Weyl group inducing Kato's original exotic Springer representation on cohomology. Our…

2020-05-07math.COmath.QAmath.RT

关于小量子群不变中心内的仿射Springer纤维

On the affine Springer fibers inside the invariant center of the small quantum group

EPFL（洛桑联邦理工学院）；Aalto University（阿尔托大学）

本文通过几何方法计算了小量子群中心中G∨不变部分的维数，并在G=SL_n情形下研究了双分次细化。

2026-05-28math.AGmath.QAmath.RT

两行 Delta Springer 簇

Two-row Delta Springer varieties

本文研究两行分拆对应的 $Δ$-Springer 簇，给出其不可约分量的显式组合描述，并与普通及奇异 Springer 纤维比较，同时把同调上的对称群作用扩展为退化仿射 Hecke 代数作用并联系 $\mathfrak{gl}_{2}$-张量空间。

2025-04-24math.COmath.QAmath.RT

更多相关论文收起更多论文

Traces on finite W-algebras

We compute the space of Poisson traces on a classical W-algebra modulo an arbitrary central character, i.e., linear functionals on such an algebra invariant under Hamiltonian derivations. This space identifies with the top cohomology of the corresponding Springer fiber. As a consequence, we deduce that the zeroth Hochschild homology of the corresponding quantum W-algebra modulo a central character identifies with the top cohomology of the corresponding Springer fiber. This implies that the number of irreducible finite-dimensional representations of this algebra is bounded by the dimension of t…

2010-05-14math.KTmath.QAmath.RT

Highest weight modules at the critical level and noncommutative Springer resolution

In arXiv:1001.2562 a certain non-commutative algebra $A$ was defined starting from a semi-simple algebraic group, so that the derived category of $A$-modules is equivalent to the derived category of coherent sheaves on the Springer (or Grothendieck-Springer) resolution. Let $\hat{\g}$ be the affine Lie algebra corresponding to the Langlands dual Lie algebra. Using results of Frenkel and Gaitsgory arXiv:0712.0788 we show that the category of $\hat{\g}$ modules at the critical level which are Iwahori integrable and have a fixed central character, is equivalent to the category of modules over a q…

2011-12-29math.QAmath.RT

Generalized affine Springer theory and Hilbert schemes on planar curves

We show that Hilbert schemes of planar curve singularities and their parabolic variants can be interpreted as certain generalized affine Springer fibers for $GL_n$, as defined by Goresky-Kottwitz-MacPherson. Using a generalization of affine Springer theory for Braverman-Finkelberg-Nakajima's Coulomb branch algebras, we construct a rational Cherednik algebra action on the homology of the Hilbert schemes, and compute it in examples. Along the way, we generalize to the parahoric setting the recent construction of Hilburn-Kamnitzer-Weekes, which may be of independent interest. In the spherical cas…

2022-01-27hep-thmath-phmath.AG

Categorification of level two representations of quantum sl(N) via generalized arc rings

We build extensions of the arc rings, relate their centers to the cohomology rings of the Springer varieties, and categorify all level two representations of quantum sl(N).

2006-11-01math.GTmath.QA

Odd Khovanov's arc algebra

We construct an odd version of Khovanov's arc algebra $H^n$. Extending the center to elements that anticommute, we get a subalgebra that is isomorphic to the oddification of the cohomology of the $(n,n)$-Springer varieties. We also prove that the odd arc algebra can be twisted into an associative algebra.

2017-06-06math.QA

A geometric realization of the center of the small quantum group

We propose a new geometric model for the center of the small quantum group using the cohomology of certain affine Springer fibers. More precisely, we establish an isomorphism between the equivariant cohomology of affine Spaltenstein fibers for a split element and the center of the deformed graded modules for the small quantum group. We also obtain an embedding from the invariant part of the nonequivariant cohomology under the action of the extended affine Weyl group to the invariant part of the center of the small quantum group under Langlands dual group action, which we conjecture to be an is…

2023-01-17math.QAmath.RT

An oddification of Khovanov's arc algebras

In this master thesis we construct an oddification of the rings $H^n$ from arXiv:math/0103190 using the functor from arXiv:0710.4300 . This leads to a collection of non-associative rings $OH^n_C$ where $C$ represent some choices of signs. Extending the center up to anti-commutative elements, we get a ring $OZ(OH^n_C)$ which is isomorphic to the oddification of the ring cohomology of the $(n,n)$-Springer variety from arXiv:1203.0797 .

2015-10-22math.QA