Some Calculations of the Lusztig-Vogan Bijection for Classical Nilpotent Orbits

TL;DR

This paper explicitly computes the Lusztig-Vogan bijection for certain classical nilpotent orbits and proves a related conjecture on regular functions of their covers, advancing understanding in representation theory.

Contribution

It provides explicit calculations of the Lusztig-Vogan bijection for specific classical nilpotent orbits and confirms a conjecture regarding regular functions of their covers.

Findings

Explicit Lusztig-Vogan bijection for some classical nilpotent orbits

Proof of Achar and Sommers' conjecture on regular functions

Enhanced understanding of classical nilpotent orbit covers

Abstract

In this manuscript, we compute explicitly the Lusztig-Vogan bijection for local systems of some classical, special, nilpotent orbits. Using these results, we prove a conjecture of Achar and Sommers on regular functions of some covers of classical nilpotent orbits.