Supercharacter theories of type A unipotent radicals and unipotent polytopes
Copyright policy )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.
Ordinary representations and characters, supercharacters, integral polytopes, Representations of finite groups of Lie type, lattice polytopes, unipotent radicals, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), finite unipotent groups, Representation Theory (math.RT), 05E10, unipotent groups, Mathematics - Representation Theory
Ordinary representations and characters, supercharacters, integral polytopes, Representations of finite groups of Lie type, lattice polytopes, unipotent radicals, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), finite unipotent groups, Representation Theory (math.RT), 05E10, unipotent groups, Mathematics - Representation Theory
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