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Endotrivial modules for the symmetric and alternating groups

Published online by Cambridge University Press:  02 February 2009

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.

Information

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2009