Weight multiplicity formulas for bivariate representations of classical Lie algebras

TL;DR

This paper derives explicit formulas for the weight multiplicities of bivariate representations in classical Lie algebras, enhancing understanding of their structure and representation theory.

Contribution

It provides a new explicit expression for weight multiplicities of bivariate representations in classical Lie algebras, which was previously not well-understood.

Findings

Derived explicit weight multiplicity formulas for bivariate representations

Enhanced understanding of classical Lie algebra representations

Facilitates further research in representation theory

Abstract

A bivariate representation of a complex simple Lie algebra is an irreducible representation having highest weight a combination of the first two fundamental weights. For a complex classical Lie algebra, we establish an expression for the weight multiplicities of bivariate representations.