Growth of cross-characteristic representations of finite quasisimple groups of Lie type
Copyright policy )Growth of cross-characteristic representations of finite quasisimple groups of Lie type
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.
- Imperial College London United Kingdom
- Durham University United Kingdom
character degrees, Modular representations and characters, Representations of finite groups of Lie type, Group Theory (math.GR), finite quasisimple groups of Lie type, finite classical groups, FOS: Mathematics, Simple groups: alternating groups and groups of Lie type, maximal subgroups, Representation Theory (math.RT), Classical groups., Arithmetic and combinatorial problems involving abstract finite groups, Conjugacy classes for groups, numbers of conjugacy classes, numbers of irreducible representations, cross-characteristic representations, Classical groups, Maximal subgroups, representation growth, 20C33, Representation growth, Mathematics - Group Theory, Mathematics - Representation Theory
character degrees, Modular representations and characters, Representations of finite groups of Lie type, Group Theory (math.GR), finite quasisimple groups of Lie type, finite classical groups, FOS: Mathematics, Simple groups: alternating groups and groups of Lie type, maximal subgroups, Representation Theory (math.RT), Classical groups., Arithmetic and combinatorial problems involving abstract finite groups, Conjugacy classes for groups, numbers of conjugacy classes, numbers of irreducible representations, cross-characteristic representations, Classical groups, Maximal subgroups, representation growth, 20C33, Representation growth, Mathematics - Group Theory, Mathematics - Representation Theory
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