Characteristic identities for Lie (super)algebras

TL;DR

This paper reviews characteristic identities for Lie (super)algebras and demonstrates their use in deriving matrix elements of finite-dimensional representations, focusing on general linear Lie algebras and superalgebras.

Contribution

It provides an overview of methods using characteristic identities to compute matrix elements in Lie (super)algebra representations, with illustrative examples.

Findings

Characteristic identities facilitate the calculation of matrix elements.

Methods are demonstrated on general linear Lie algebras and superalgebras.

The overview aids in understanding representation theory techniques.

Abstract

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the theory, we look at the examples of the general linear Lie algebras and Lie superalgebras.