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.
Accepted: 2017-08-18
Published online: 2018-01-29
DOI: https://doi.org/10.5802/alco.3
Classification: 05E10, 20C33
Keywords: supercharacters, integral polytopes, finite unipotent groups, unipotent radicals
@article{ALCO_2018__1_1_23_0, author = {Thiem, Nathaniel}, title = {Supercharacter theories of type <span class="mathjax-formula">$A$</span> unipotent radicals and unipotent polytopes}, journal = {Algebraic Combinatorics}, pages = {23--45}, publisher = {MathOA foundation}, volume = {1}, number = {1}, year = {2018}, doi = {10.5802/alco.3}, zbl = {06882333}, mrnumber = {3857158}, language = {en}, url = {alco.centre-mersenne.org/item/ALCO_2018__1_1_23_0/} }
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/item/ALCO_2018__1_1_23_0/
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