Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements
Combinatorics
2025-07-14 v2
Abstract
Given a permutation, there is a well-developed literature studying the number of ways one can factor it into a product of other permutations subject to certain conditions. We initiate the analogous theory for the type A Iwahori-Hecke algebra by generalizing the notion of factorization in terms of the Jucys-Murphy elements. Some of the oldest and most foundational factorization results for the symmetric groups pertain to the long cycle. Our main results give q-deformations of these long cycle factorizations and reveal q-binomial, q-Catalan, and q-Narayana numbers along the way.
Cite
@article{arxiv.2506.08883,
title = {Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements},
author = {Jose Bastidas and Sarah Brauner and Mathieu Guay-Paquet and Alejandro H. Morales and GaYee Park and Franco Saliola},
journal= {arXiv preprint arXiv:2506.08883},
year = {2025}
}
Comments
minor edits