2015/12/10 by Nathaniel Thiem, Thiem, Nathaniel
Computer Science · Engineering · Mathematics · #semigroups and automata theory #graph theory and CDMA systems #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.1512.03446
Even with the introduction of supercharacter theories, the representation\ntheory of many unipotent groups remains mysterious. This paper constructs a\nfamily of supercharacter theories for normal pattern groups in a way that\nexhibit many of the combinatorial properties of the set partition combinatorics\nof the full uni-triangular groups, including combinatorial indexing sets,\ndimensions, and computable character formulas. Associated with these\nsupercharacter theories is also a family of polytopes whose integer lattice\npoints give the theories geometric underpinnings.\n