On the restriction of cross characteristic representations of ^2F_4(q) to proper subgroups

Details On the restriction of cross characteristic representations of ^2F_4(q) to proper subgroups On the restriction of cross characteristic representations of ^2F_4(q) to proper subgroups

2009-10-25

arxiv.org/abs/0910.4758v1

Mathematics

Representation Theory

9 pages. Arch. d. Math, to appear

Scientific paper

We prove that the restriction of any nontrivial representation of the Ree groups $^2F_{4}(q), q=2^{2n+1}\geq8$ in odd characteristic to any proper subgroup is reducible. We also determine all triples $(K, V, H)$ such that $K \in \{^2F_4(2), ^2F_4(2)'\}$, $H$ is a proper subgroup of $K$, and $V$ is a representation of $K$ in odd characteristic restricting absolutely irreducibly to $H$.

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