Supercharacter theories constructed by the method of little groups

Abstract

The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of semidirect products with abelian normal subgroups. In particular, we apply this construction to reproduce known supercharacter theories of several families of unipotent groups. We also utilize our method to construct a collection of new supercharacter theories of the unipotent upper-triangular matrices.

24 pages

References in corpus (5)

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• Representations of Finite Unipotent Linear Groups by the Method of Clusters
• A Supercharacter Analogue for Normality
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Cited by in corpus (4)

• Restriction and induction for supercharacters of finite groups of triangular type
• Supercharacter theories for Sylow $p$-subgroups of Lie type $G_2$
• A supercharacter theory for Sylow $p$-subgroups of the Steinberg triality groups
• Supercharacter theories for Sylow $p$-subgroups of the Ree groups