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Transactions of the American Mathematical Society

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


Authors: Christine Bessenrodt and Jørn B. Olsson
Journal: Trans. Amer. Math. Soc. 358 (2006), 3623-3635
MSC (2000): Primary 20C30; Secondary 20C25
DOI: https://doi.org/10.1090/S0002-9947-05-03809-2
Published electronically: December 20, 2005
MathSciNet review: 2218991
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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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Additional Information

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

Jørn B. Olsson
Affiliation: Matematisk Afdeling, University of Copenhagen, Copenhagen, Denmark
Email: olsson@math.ku.dk

DOI: https://doi.org/10.1090/S0002-9947-05-03809-2
Received by editor(s): December 15, 2003
Received by editor(s) in revised form: August 18, 2004, and August 20, 2004
Published electronically: December 20, 2005
Additional Notes: This work was partially supported by The Danish National Research Council.
Dedicated: To our friend Alun Morris on the occasion of his 70th birthday
Article copyright: © Copyright 2005 by the authors

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