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

Abstract

We prove that the restriction of any nontrivial representation of the Ree groups ${}^2{F}_4(q),q=2^{2n+1}\ge 8$ in odd characteristic to any proper subgroup is reducible. We also determine all triples $(K,V,H)$ such that $K\in {\{}^2{F}_4(2){,}^2{F}_4(2{)}^{\prime }\}$, $H$ is a proper subgroup of $K$, and $V$ is a representation of $K$ in odd characteristic restricting absolutely irreducibly to $H$.

9 pages. Arch. d. Math, to appear