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arXiv:math/0111306 [math.RT]AbstractReferencesReviewsResources

Cartan Determinants and Shapovalov forms

Jonathan Brundan, Alexander Kleshchev

Published 2001-11-29Version 1

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 $p$-blocks of the symmetric group and its double cover, and of the associated Hecke algebras at roots of unity.

Journal: Math. Ann. 324 (2002), 431-449.
Categories: math.RT
Subjects: 17B67, 20G05
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