Positivity and Web Bases for Specht Modules of Hecke Algebras

2022/07/01 by Samuel David Heard, Heard, Samuel David, Jonathan R. Kujawa +1
Chemistry · Mathematics · #05E10 #20C08 #20C30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2207.00654

openalex publication_date 2022/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the transition matrix from the standard basis to the web basis for a Specht module of the Hecke algebra is unitriangular and satisfies a strong positivity property whenever the Specht module is labeled by a partition with at most two parts. This generalizes results of Russell--Tymoczko and Rhoades.

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