Branching rules in the ring of superclass functions of unipotent upper-triangular matrices

By Nathaniel Thiem. 2008

55 citations recorded by the source corpus.

It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical representation theory of the symmetric group. This paper begins by exploring a connection to the ring of symmetric functions in non-commuting variables that mirrors the symmetric group’s relationship with the ring of symmetric functions. It then also investigates some of the representation theoretic structure constants arising from the restriction, tensor products and superinduction of supercharacters in this context.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/ed0b0f99627f851357d94d69d1bd272f2c9fd508

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

Citations in the corpus

Ramanujan sums as supercharacters (2012, background): “Other recent work on supercharacters concerns connections with Schur rings [23,25] and with their combinatorial properties [15, 60, 61].”
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (2010, methodology): “(b) There is an algorithmic method for computing restrictions of supercharacters (and also tensor products of characters) [37,38].”