Séminaire Lotharingien de Combinatoire, 78B.9 (2017), 12 pp.
Supercharacter Theories of Type A Unipotent Radicals and Unipotent Polytopes
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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