Rigidity of formal character of Lie algebras of type A

TL;DR

This paper proves that certain formal characters of Weyl modules for complex simple Lie algebras of type A are uniquely determined by natural conditions, demonstrating a rigidity property.

Contribution

It establishes a rigidity result showing that formal characters of Weyl modules are uniquely characterized by two natural conditions for Lie algebras of type A.

Findings

Formal characters are uniquely determined by natural conditions.

The result applies specifically to Lie algebras of type A.

It confirms the rigidity of the formal character characterization.

Abstract

For a complex simple Lie algebra of type $A$, given a family of elements $f_\lambda\in \mathbb Z[\Lambda],\lambda\in \Lambda^+,$ we show that $f_\lambda$ is just the formal character of the Weyl module $V(\lambda) $ if $f_\lambda$ satisfy two natural conditions.