Braid relations for involution words in affine Coxeter groups

2017/03/30 by Eric Marberg, Marberg, Eric
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1703.10437

openalex publication_date 2017/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe an algorithm to identify a minimal set of "braid relations" which span and preserve all sets of involution words for twisted Coxeter systems of finite or affine type. We classify the cases in which adding the smallest possible set of "half-braid" relations to the ordinary braid relations produces a spanning set: in the untwisted case, this occurs for the Coxeter systems which are finite with rank two or type A_n, or affine with rank three or type A_n. These results generalize recent work of Hu and Zhang on the finite classical cases.

Citations

• A bar operator for involutions in a Coxeter group

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