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endotrivial modules

Proceedings of the Edinburgh Mathematical Society (1)

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Endotrivial modules for the symmetric and alternating groups
Part of
- Representation theory of groups
Jon F. Carlson, Nadia Mazza, Daniel K. Nakano
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 1 / February 2009

Published online by Cambridge University Press:

02 February 2009, pp. 45-66
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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.