Stratified hyperkahler spaces from semisimple Lie algebras

TL;DR

This paper investigates the structure of singular hyperkahler quotients derived from the cotangent bundle of complex semisimple Lie groups, revealing stratified hyperkahler spaces with explicitly describable stratification.

Contribution

It provides a detailed analysis of stratified hyperkahler spaces arising from semisimple Lie groups, especially in cases with explicit stratification descriptions.

Findings

Stratified hyperkahler spaces have a well-defined stratification satisfying the frontier condition.

The stratification can be explicitly described using Lie theoretic data.

The study enhances understanding of singular hyperkahler quotients in geometric representation theory.

Abstract

We study singular hyperkahler quotients of the cotangent bundle of a complex semisimple Lie group as stratified spaces whose strata are hyperkahler. We focus on one particular case where the stratification satisfies the frontier condition and the partial order on the set of strata can be described explicitly by Lie theoretic data.