On Cartan matrices and lower defect groups for covering groups of symmetric groups

Bessenrodt, Christine; Olsson, Jørn

doi:10.1090/S0002-9947-05-03809-2

On Cartan matrices and lower defect groups for covering groups of symmetric groups
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by Christine Bessenrodt and Jørn B. Olsson PDF

Trans. Amer. Math. Soc. 358 (2006), 3623-3635

Abstract:

We determine the elementary divisors of the Cartan matrices of spin $p$-blocks of the covering groups of the symmetric groups when $p$ is an odd prime. As a consequence, we also compute the determinants of these Cartan matrices, and in particular we confirm a conjecture by Brundan and Kleshchev that these determinants depend only on the weight but not on the sign of the block.

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