2007/12/07 by Nathaniel Thiem, Thiem, Nathaniel, Vidya Venkateswaran +1
Computer Science · Engineering · #20C99 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0712.1237
openalex publication_date 2007/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that the representation theory of the finite group of unipotent upper-triangular matrices Un over a finite field is a wild problem. By instead considering approximately irreducible representations (supercharacters), one obtains a rich combinatorial theory analogous to that of the symmetric group, where we replace partition combinatorics with set-partitions. This paper studies the supercharacter theory of a family of subgroups that interpolate between Un-1 and Un. We supply several combinatorial indexing sets for the supercharacters, supercharacter formulas for these indexing sets, and a combinatorial rule for restricting supercharacters from one group to another. A consequence of this analysis is a Pieri-like restriction rule from Un to Un-1 that can be described on set-partitions (analogous to the corresponding symmetric group rule on partitions).