Exotic symmetric space over a finite field, II

TL;DR

This paper proves a conjecture relating intersection cohomology Poincare polynomials of exotic symmetric space orbit closures to modified Kostka polynomials, using character sheaves theory, extending prior work with a new approach.

Contribution

It provides a new proof of a conjecture connecting intersection cohomology and Kostka polynomials via character sheaves, offering an alternative to Kato's earlier proof.

Findings

Confirmed the conjecture for exotic symmetric spaces.

Established a new method using character sheaves.

Connected geometric and combinatorial invariants.

Abstract

This paper is the second part of the papers in the same title. In this paper, we prove a conjecture of Achar-Henderson, which asserts that the Poincare polynomials of the intersection cohomology complex associated to the closure of Sp_{2n}-orbits in the Kato's exotic nilpotent cone coincide with the modified Kostka polynomials indexed by double partitions, introduced by the first author. Actually this conjecture was recently proved by Kato by a different method. Our approach is based on the theory of character sheaves on the exotic symmetric space.