Cartan Determinants and Shapovalov forms
Representation Theory
2007-05-23 v1
Abstract
We compute the determinant of the Gram matrix of the Shapovalov form on weight spaces of the basic representation of an affine Kac-Moody algebra of ADE type (possibly twisted). As a consequence, we obtain explicit formulae for the determinants of the Cartan matrices of -blocks of the symmetric group and its double cover, and of the associated Hecke algebras at roots of unity.
Cite
@article{arxiv.math/0111306,
title = {Cartan Determinants and Shapovalov forms},
author = {Jonathan Brundan and Alexander Kleshchev},
journal= {arXiv preprint arXiv:math/0111306},
year = {2007}
}