Interpolating between promotion and the long cycle
Bruce W. Westbury
TL;DR
This paper presents a novel proof of the cyclic sieving phenomenon related to promotion on rectangular standard tableaux, utilizing cactus group actions within the seminormal bases of Hecke algebra representations.
Contribution
It introduces a new proof technique for cyclic sieving phenomena using cactus group actions in the context of Hecke algebra representations.
Findings
New proof of cyclic sieving for promotion on rectangular tableaux
Application of cactus group actions in representation theory
Enhanced understanding of algebraic structures in combinatorics
Abstract
We give a new proof of the cyclic sieving phenomena for promotion on rectangular standard tableaux. This uses an action of the cactus groups in the seminormal bases of the irreducible representations of the Hecke algebras.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic structures and combinatorial models