ALGEBRAIC COMBINATORICS

no. 1

Supercharacter theories of type A unipotent radicals and unipotent polytopes
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: 2017-08-15
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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