Annihilators and associated varieties of Harish-Chandra modules for $SO^*(2n)$

TL;DR

This paper develops combinatorial methods to determine the annihilator and associated variety of simple Harish-Chandra modules for the group $SO^*(2n)$ with trivial infinitesimal character, using signed involutions and tableaux.

Contribution

It introduces explicit combinatorial recipes linking signed involutions to tableaux for analyzing Harish-Chandra modules of $SO^*(2n)$.

Findings

Provides a method to read off annihilators from tableaux.

Establishes a correspondence between signed involutions and module invariants.

Enhances understanding of representation theory for $SO^*(2n)$.

Abstract

Given a simple Harish-Chandra module for this group of trivial infinitesimal character, parametrized by a signed involution, we produce combinatorial recipes for attaching to it a pair of tableaux from which its annihilator and associated variety can be read off.