Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911049813327872 |
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| author | Bastidas, Jose Brauner, Sarah Guay-Paquet, Mathieu Morales, Alejandro H. Park, GaYee Saliola, Franco |
| author_facet | Bastidas, Jose Brauner, Sarah Guay-Paquet, Mathieu Morales, Alejandro H. Park, GaYee Saliola, Franco |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_08883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements Bastidas, Jose Brauner, Sarah Guay-Paquet, Mathieu Morales, Alejandro H. Park, GaYee Saliola, Franco Combinatorics 20C08, 05A05, 05A15, 05A30, 05E05 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. |
| title | Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements |
| topic | Combinatorics 20C08, 05A05, 05A15, 05A30, 05E05 |
| url | https://arxiv.org/abs/2506.08883 |