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arXiv · 2506.08883

Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements

Jose Bastidas·Sarah Brauner·Mathieu Guay-Paquet·Alejandro H. Morales·GaYee Park·Franco Saliola
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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.

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Jose Bastidas, Sarah Brauner, Mathieu Guay-Paquet, Alejandro H. Morales, GaYee Park, Franco Saliola. 2025-06-10. Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements. https://arxiv.org/abs/2506.08883

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