Transactions of the American Mathematical Society

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

Author(s): Christine Bessenrodt; Jørn B. Olsson
Journal: Trans. Amer. Math. Soc. 358 (2006), 3623-3635.
MSC (2000): Primary 20C30; Secondary 20C25
Posted: December 20, 2005
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Abstract: We determine the elementary divisors of the Cartan matrices of spin

-blocks of the covering groups of the symmetric groups when

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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Christine Bessenrodt
Affiliation: Institut für Mathematik, Universität Hannover, D-30167 Hannover, Germany
Email: bessen@math.uni-hannover.de

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