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Supercharacter theories of type A unipotent radicals and unipotent polytopes
Thiem, Nathaniel1
1 University of Colorado Boulder Department of Mathematics Campus Box 395 Boulder, Colorado 80309 (USA)
Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 23-45.

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:
Accepted:
Published online:
DOI: 10.5802/alco.3
Classification: 05E10, 20C33
Keywords: supercharacters, integral polytopes, finite unipotent groups, unipotent radicals

Thiem, Nathaniel 1

1 University of Colorado Boulder Department of Mathematics Campus Box 395 Boulder, Colorado 80309 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Thiem, Nathaniel. Supercharacter theories of type $A$ unipotent radicals and unipotent polytopes. Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 23-45. doi : 10.5802/alco.3. https://alco.centre-mersenne.org/articles/10.5802/alco.3/

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