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Endotrivial modules for the symmetric and alternating groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  02 February 2009

Jon F. Carlson ,
Nadia Mazza  and
Daniel K. Nakano
Jon F. Carlson
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA (jfc@math.uga.edu; nakano@math.uga.edu)
Nadia Mazza
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, UK
Daniel K. Nakano
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA (jfc@math.uga.edu; nakano@math.uga.edu)
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Abstract

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In this paper we determine the group of endotrivial modules for certain symmetric and alternating groups in characteristic p. If p = 2, then the group is generated by the class of Ωn(k) except in a few low degrees. If p > 2, then the group is only determined for degrees less than p2. In these cases we show that there are several Young modules which are endotrivial.

Keywords

endotrivial modulesYoung modulessymmetric groupsalternating groups

MSC classification

Secondary: 20C20: Modular representations and characters 20C30: Representations of finite symmetric groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 45 - 66
Copyright
Copyright © Edinburgh Mathematical Society 2009