Non-integral representation theory of even multiplicity finite W-algebras

TL;DR

This paper completes the classification of finite-dimensional irreducible representations of finite W-algebras related to even multiplicity nilpotent elements in classical Lie algebras, extending previous work on integral central characters.

Contribution

It extends the classification of representations of finite W-algebras to include non-integral central characters for even multiplicity nilpotent elements.

Findings

Complete classification of finite-dimensional irreducible representations for non-integral central characters.

Extension of previous classifications from integral to non-integral cases.

Provides a comprehensive understanding of representations associated with even multiplicity nilpotent elements.

Abstract

We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is determined for such representations of integral central character.