The $q$-deformed random-to-random family in the Hecke algebra
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909909234221056 |
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| author | Brauner, Sarah Commins, Patricia Grinberg, Darij Saliola, Franco |
| author_facet | Brauner, Sarah Commins, Patricia Grinberg, Darij Saliola, Franco |
| contents | We generalize Reiner--Saliola--Welker's well-known but mysterious family of *$k$-random-to-random shuffles* from Markov chains on symmetric groups to Markov chains on the Type-$A$ Iwahori--Hecke algebras. We prove that the family of operators pairwise commutes and has eigenvalues that are polynomials in $q$ with non-negative integer coefficients. Our work generalizes work of Reiner--Saliola--Welker and Lafrenière for the symmetric group, and simplifies all known proofs in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $q$-deformed random-to-random family in the Hecke algebra Brauner, Sarah Commins, Patricia Grinberg, Darij Saliola, Franco Combinatorics Rings and Algebras Representation Theory 20C08, 20C30, 60J10, 05E10 We generalize Reiner--Saliola--Welker's well-known but mysterious family of *$k$-random-to-random shuffles* from Markov chains on symmetric groups to Markov chains on the Type-$A$ Iwahori--Hecke algebras. We prove that the family of operators pairwise commutes and has eigenvalues that are polynomials in $q$ with non-negative integer coefficients. Our work generalizes work of Reiner--Saliola--Welker and Lafrenière for the symmetric group, and simplifies all known proofs in this case. |
| title | The $q$-deformed random-to-random family in the Hecke algebra |
| topic | Combinatorics Rings and Algebras Representation Theory 20C08, 20C30, 60J10, 05E10 |
| url | https://arxiv.org/abs/2503.17580 |