Publications and Preprints

1. Hikita conjecture for classical Lie algebras. Advances in Mathematics, minor revision requested. [arXiv:2409.13914]

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

2. Geometry of the fixed points loci and discretization of Springer fibers in classical types.  Preprint. [arXiv:2405.10105]

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. 

3. The action of component groups on irreducible components of Springer fibers. Submitted

I describe the stabilizers of this action, and use the description to prove a conjecture of Lusztig and Sommers. The result gives 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.

4. Around Hikita-Nakajima conjecture for nilpotent orbits and parabolic Slodowy varieties, joined with Vasily Krylov, and Dmytro Matvieievskyi.  Preprint. [arXiv:2410.20512]

With Vasily Krylov and Dmytro Matvieievskyi, we study several versions of the Hikita–Nakajima conjecture for nilpotent orbits and parabolic Slodowy varieties. We give a counterexample and propose a modified statement. The key technique is a comparison between the weights appearing in the category O of a parabolic W-algebra and the torus fixed points on the dual side, which reflects the symplectic duality between the pair.

In Preparation

1. Affine Springer fibers and Slodowy varieties. Joint with Pablo Boixeda Alvarez.

Expository notes

1. MV Slices and MV isomorphism, A talk from the learning seminar on i-Coulomb branches. For the quantum MV isomorphisms, please see the note/talk on seminar website.

2. Introduction to affine Springer fiber, this is a talk from A talk from our learning seminar on affine Springer fibers. 

3. On orbits of connected components of a fixed point variety of the Springer fiber. This will be a part of a paper in preparation.