Tensor product Markov chains
File(s)
Accepted version
Author(s)
Benkart, Georgia
Diaconis, Persi
Liebeck, Martin
Tiep, Pham Huu
Type
Journal Article
Abstract
We analyze families of Markov chains that arise from decomposing ten-sor products of irreducible representations. This illuminates the Burnside-Brauer Theorem for building irreducible representations, the McKay Corre-spondence, and Pitman’s2M−XTheorem. The chains are explicitly di-agonalizable, and we use the eigenvalues/eigenvectors to give sharp rates ofconvergence for the associated random walks. For modular representations,the chains are not reversible, and the analytical details are surprisingly intri-cate. In the quantum group case, the chains fail to be diagonalizable, but anovel analysis using generalized eigenvectors proves successful.
Date Issued
2020-11-01
Date Acceptance
2019-03-25
Citation
Journal of Algebra, 2020, 561, pp.17-83
ISSN
0021-8693
Publisher
Elsevier
Start Page
17
End Page
83
Journal / Book Title
Journal of Algebra
Volume
561
Copyright Statement
© 2019 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
Science & Technology
Physical Sciences
Mathematics
Tensor product
Markov chain
McKay correspondence
Modular representation
Brauer character
Quantum group
RANDOM-WALKS
STEINS METHOD
REPRESENTATIONS
CHARACTER
CONVERGENCE
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2019-11-13