I was just wondering if there exists such a formula. Specifically I need to calculate characters of irreducible representations of GSp$(4,\mathbb{C})$.
I know how to do it for the compact Lie group Sp$(4,\mathbb{C})$. Is there a way to extend this to account for GSp$(4,\mathbb{C})$?
I know the structure of the roots and weights for GSp$(4,\mathbb{C})$ so is it ok to just use the WCF blindly in this situation?
Also what would the Weyl group be?