Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2407.08644 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911188110016512 |
|---|---|
| author | Axelrod-Freed, Ilani Brauner, Sarah Chiang, Judy Hsin-Hui Commins, Patricia Lang, Veronica |
| author_facet | Axelrod-Freed, Ilani Brauner, Sarah Chiang, Judy Hsin-Hui Commins, Patricia Lang, Veronica |
| contents | We generalize random-to-random shuffling from a Markov chain on the symmetric group to one on the Type A Iwahori Hecke algebra, and show that its eigenvalues are polynomials in q with non-negative integer coefficients. Setting q=1 recovers results of Dieker and Saliola, whose computation of the spectrum of random-to-random in the symmetric group resolved a nearly 20 year old conjecture by Uyemura-Reyes. Our methods simplify their proofs by drawing novel connections to the Jucys-Murphy elements of the Hecke algebra, Young seminormal forms, and the Okounkov-Vershik approach to representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectrum of random-to-random shuffling in the Hecke algebra Axelrod-Freed, Ilani Brauner, Sarah Chiang, Judy Hsin-Hui Commins, Patricia Lang, Veronica Combinatorics Probability Representation Theory 05E10, 60J10, 20C08 We generalize random-to-random shuffling from a Markov chain on the symmetric group to one on the Type A Iwahori Hecke algebra, and show that its eigenvalues are polynomials in q with non-negative integer coefficients. Setting q=1 recovers results of Dieker and Saliola, whose computation of the spectrum of random-to-random in the symmetric group resolved a nearly 20 year old conjecture by Uyemura-Reyes. Our methods simplify their proofs by drawing novel connections to the Jucys-Murphy elements of the Hecke algebra, Young seminormal forms, and the Okounkov-Vershik approach to representation theory. |
| title | Spectrum of random-to-random shuffling in the Hecke algebra |
| topic | Combinatorics Probability Representation Theory 05E10, 60J10, 20C08 |
| url | https://arxiv.org/abs/2407.08644 |