Admissible modules and normality of classical nilpotent orbits II

TL;DR

This paper computes character formulas for classical nilpotent varieties, enabling the determination of K-type multiplicities in the ring of regular functions, advancing understanding of their representation-theoretic structure.

Contribution

It provides explicit character formulas for Brylinski models of all classical nilpotent varieties, a novel comprehensive computation in this area.

Findings

Character formulas for Brylinski models of all classical nilpotent varieties.

Explicit computation of K-type multiplicities in the ring of regular functions.

Enhanced understanding of the representation theory of classical nilpotent orbits.

Abstract

In this paper, we compute the character formula of the Brylinski model for all classical nilpotent varieties $\overline{\mathcal{O}}$. As a consequence, one can compute the multiplicities of all $K-$types of the ring of regular functions $R(\overline{\mathcal{O}})$ for all classical nilpotent varieties.