Growth of cross-characteristic representations of finite quasisimple groups of Lie type

Details Growth of cross-characteristic representations of finite quasisimple groups of Lie type Growth of cross-characteristic representations of finite quasisimple groups of Lie type

2011-12-16

arxiv.org/abs/1112.3941v1

Mathematics

Representation Theory

Scientific paper

In this paper we give a bound to the number of conjugacy classes of maximal subgroups of any almost simple group whose socle is a classical group of Lie type. The bound is $2n^{5.2}+n\log_2\log_2 q$, where $n$ is the dimension of the classical socle and $q$ is the size of the defining field. To obtain the bound, we first bound the number of projective cross-characteristic representations of simple groups of Lie type as a function of the representation degree. These bounds are computed for different families of groups separately. In the computation, we use information on class numbers, minimal character degrees and gaps between character degrees.

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