Supercharacter formulas for pattern groups

By Persi Diaconis, Nathaniel Thiem. 2006

55 citations recorded by the source corpus.

C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group U n (F q ). In this theory superclasses are certain unions of conjugacy classes, and supercharacters are a set of characters which are constant on superclasses. This paper gives a character formula for a supercharacter evaluated at a superclass for pattern groups and more generally for algebra groups.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/9931e88c4f380af9db8675882692bc0da719d528

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In Artificial Intelligence

In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

Citations in the corpus

Branching rules in the ring of superclass functions of unipotent upper-triangular matrices (2008, background): “1) where τμ(i l) = 0 if i l / ∈ A(μ) (see [11] for the corresponding formula for arbitrary pattern groups).”
The Markov chain Monte Carlo revolution (2008, methodology): “The detailed use of this required new formula [4] and leads to an extension of the theory to algebra groups in joint work with Isaacs and Theme [22, 34].”
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].”