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.

Key Words:

• Supercharacter
• Unipotent group

2010 Mathematics Subject Classification:

• 20C33
• 05E10

ACKNOWLEDGMENTS

I would like to thank Nat Thiem, as well as the anonymous referee, for their numerous helpful suggestions and insights.