Séminaire Lotharingien de Combinatoire, 78B.9 (2017), 12 pp.

Nathaniel Thiem

Supercharacter Theories of Type A Unipotent Radicals and Unipotent Polytopes

Abstract. Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of the combinatorial properties of the set partition combinatorics of the full uni-triangular groups, including combinatorial indexing sets, dimensions, and computable character formulas. Associated with these supercharacter theories is also a family of polytopes whose integer lattice points give the theories geometric underpinnings.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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