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arXiv · 1512.03446

Supercharacter theories of type $A$ unipotent radicals and unipotent polytopes

Nathaniel Thiem
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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.

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Nathaniel Thiem. 2015-12-10. Supercharacter theories of type $A$ unipotent radicals and unipotent polytopes. https://arxiv.org/abs/1512.03446

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