Rigidity of formal character of Lie algebras of type A

Zhongguo Zhou

Published 2012-02-20, updated 2012-02-22Version 2

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.