1. Spectrum of random-to-random shuffling in the Hecke algebra
- Author
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Axelrod-Freed, Ilani, Brauner, Sarah, Chiang, Judy Hsin-Hui, Commins, Patricia, and Lang, Veronica
- Subjects
Mathematics - Combinatorics ,Mathematics - Probability ,Mathematics - Representation Theory ,05E10, 60J10, 20C08 - Abstract
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., Comment: Reorganized, streamlined arguments, improved exposition, and addressed/clarified subtleties from v1
- Published
- 2024