Preprint
The $q$-Deformed Random-to-Random Family in the Hecke Algebra
2025
Abstract
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.
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Details
- Title
- The $q$-Deformed Random-to-Random Family in the Hecke Algebra
- Creators
- Sarah Brauner - Brown UniversityPatricia Commins - Brown UniversityDarij Grinberg - Drexel UniversityFranco Saliola - Université du Québec à Montréal
- Publisher
- Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022167718504721