Springer Representations on the Khovanov Springer Varieties

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

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...

Reflection Functors for Quiver Varieties and Weyl Group Actions

We define a Weyl group action on quiver varieties using reflection functors, which resemble ones introduced by Bernstein-Gelfand-Ponomarev [1]. As an application, we define Weyl group representations of homology groups of quiver varieties. They are analogues of Slodowy’s construction of Springer representations of the Weyl group.

A Hessenberg Generalization of the Garsia-Procesi Basis for the Cohomology Ring of Springer Varieties

The Springer variety is the set of flags stabilized by a nilpotent operator. In 1976, T.A. Springer observed that this variety’s cohomology ring carries a symmetric group action, and he offered a deep geometric construction of this action. Sixteen years later, Garsia and Procesi made Springer’s work more transparent and accessible by presenting the cohomology ring as a graded quotient of a poly...

Cell Decompositions of Quiver Flag Varieties for Nilpotent Representations of the Oriented Cycle

Generalizing Schubert cells in type A and a cell decomposition if Springer fibres in type A found by L. Fresse we prove that varieties of complete flags in nilpotent representations of an oriented cycle admit an affine cell decomposition parametrized by multi-tableaux. We show that they carry a torus operation and describe the T -equivariant cohomology using GoreskyKottwitz-MacPherson-theory. A...