9
$\begingroup$

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?

  • 0
    How is $Sp_{4}(C)$ compact. Or, do you mean $Sp(4)$=invertible quaternioc matrices? Look here: http://en.wikipedia.org/wiki/Symplectic_group. Please adopt your notation. Is $GSp(4, \mathbb{C)}$ a real reductive Lie group, then there are analogous formulas or is a compact extension of $Sp(4,C)$? For the discrete series, Harish-Chandra has two papers solving the complete problem for all simple real Lie groups.2013-10-11

0 Answers 0