Preprints

1. Geometry of the fixed points loci and discretization of Springer fibers in classical types. 

In this paper, I propose an approach to describe the discretization of a Springer fiber, a centrally extended finite set that has appeared in different contexts of representation theory. In particular, understanding these discretization leads to explicit descriptions of left cell modules and of summands of the asymptotic affine Hecke algebra. The main result is obtained using a combination of explicit Springer correspondence, computation of equivariant K-groups, and existence of exceptional collections in the derived categories of certain Hessenberg varieties. 

2. The action of component groups on irreducible components of Springer fibers.

In this paper, I describe the stabilizers of the action mentioned in the title. The result suggests a nontrivial relation between irreducible components of Springer fibers and cells in finite Weyl groups. Related keywords: noncrossing partitions, signed domino tableaux, Lusztig's quotient.

3. Around Hikita-Nakajima conjecture for nilpotent orbits and parabolic Slodowy varieties, joined with Vasily Krylov, and Dmytro Matvieievskyi. 

4. Hikita conjecture for classical Lie algebras.

In this paper, I prove the classical Hikita conjecture for certain nilpotent orbits and Slodowy varieties. Related keywords: generalized coinvariant algebras, Pfaffian, equivariant cohomology.

Notes

1. On orbits of connected components of a fixed point variety of the Springer fiber.