Generalized Casimir Operators

TL;DR

This paper introduces a new class of central operators that generalize the Casimir operator for symmetrizable Kac-Moody Lie algebras, revealing their properties and effects on highest weight vectors.

Contribution

It defines and analyzes a novel class of central operators extending the Casimir operator in the context of symmetrizable Kac-Moody Lie algebras.

Findings

Operators move highest weight vectors to new highest weight vectors

Properties of these generalized Casimir operators are established

The operators extend the classical Casimir operator's role

Abstract

Let G be symmetrizable Kac-Moody Lie algebra. In this paper we describe a new class of central operators generalising the Casimir operator. We also prove some properties of these operators and show that these operators move highest weight vectors to new highest weight vectors.