The q-deformed random-to-random family in the Hecke algebra

2025/03/21 by Brauner, Sarah, Commins, Patricia, Grinberg, Darij +1 · 1 citation
#05E10 #20C08 #20C30 #60J10 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.17580

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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• Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements

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