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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Varieties attached to an $ {\rm SL}\sb 2(2\sp k)$-module


Author: Geoffrey Mason
Journal: Proc. Amer. Math. Soc. 116 (1992), 343-350
MSC: Primary 20G05; Secondary 14M99
MathSciNet review: 1100661
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Abstract: Let $ {G_k} = \operatorname{SL}_2({2^k})$ and $ V$ be an $ F{G_k}$-module with $ F$ a field containing $ \operatorname{GF}(2^k)$. We show that $ V$ is irreducible if and only if there is a subgroup $ {U_0}$ contained in a $ 2$-Sylow of $ {G_k}$ such that $ V$ affords the regular representation of $ {U_0}$. We further show how to construct a variety, defined over an algebraic closure of $ \operatorname{GF}(2)$, whose $ \operatorname{GF}(2^k)$-rational points parameterize those conjugacy classes of subgroups of $ {G_k}$, isomorphic to $ {U_0}$, that are not represented regularly on $ V$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1100661-3
PII: S 0002-9939(1992)1100661-3
Article copyright: © Copyright 1992 American Mathematical Society