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Preprint
The $q$-deformed random-to-random family in the Hecke algebra
21 Mar 2025
Abstract
We generalize Reiner--Saliola--Welker's well-known but mysterious family of * -random-to-random shuffles* from Markov chains on symmetric groups to Markov chains on the Type- Iwahori--Hecke algebras. We prove that the family of operators pairwise commutes and has eigenvalues that are polynomials in 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 BraunerPatricia ComminsDarij GrinbergFranco Saliola
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022042268104721