A remark on the topology of (n,n) Springer varieties

Crossingless matchings and the cohomology of (n,n) Springer varieties

The sequence of rings $H^n, n\ge 0,$ introduced in math.QA/0103190, controls categorification of the quantum sl(2) invariant of tangles. We prove that the center of $H^n$ is isomorphic to the cohomology ring of the (n,n) Springer variety and show that the braid group action in the derived category of $H^n$-modules descends to the Springer action of the symmetric group.

Oddification of the cohomology of type A Springer varieties

We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q=-1. This allows us to define graded modules over the Hecke algebra at q=-1 that are `odd' analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identified with the corresponding Specht module …

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。

Heisenberg顶点代数与阿贝尔簇

Heisenberg vertex algebras and abelian varieties

本文研究Heisenberg顶点代数在阿贝尔簇上的协变空间，并展示这些空间可推广为阿贝尔簇模空间上的扭曲D-模。通过例子表明，曲线上的协变表示可扩展到任意阿贝尔簇。

Some remarks on associated varieties of vertex operator superalgebras

We study several families of vertex operator superalgebras from a jet (super)scheme point of view. We provide new examples of vertex algebras which are "chiralizations" of their Zhu's Poisson algebras $R_V$. Our examples come from affine $C_\ell^{(1)}$-series vertex algebras ($\ell \geq 1$), certain $N=1$ superconformal vertex algebras, Feigin-Stoyanovsky principal subspaces, Feigin-Stoyanovsky type subspaces, graph vertex algebras $W_Γ$, and extended Virasoro vertex algebra. We also give a counterexample to the chiralization property for the $N=2$ superconformal vertex algebra of central char…

关于伴随簇与最小张力全息的对偶性评述

Remarks on Associated Varieties and Minimal Tension Holography

本文研究最小张力弦理论中路径积分局域化与边界顶点代数伴随簇的关系，揭示 AdS₃ 共形边界与 V₁(psl(2|2)) 伴随簇的联系，并构造 V₁(psl(4|4)) 的自由场实现以探索自由 N=4 SYM 的世界面对偶。