@article{8a8804005d8c455e8b626ffe3a823197,
title = "Tensor product Markov chains",
abstract = "We analyze families of Markov chains that arise from decomposing tensor products of irreducible representations. This illuminates the Burnside-Brauer theorem for building irreducible representations, the McKay correspondence, and Pitman's 2M−X theorem. The chains are explicitly diagonalizable, and we use the eigenvalues/eigenvectors to give sharp rates of convergence for the associated random walks. For modular representations, the chains are not reversible, and the analytical details are surprisingly intricate. In the quantum group case, the chains fail to be diagonalizable, but a novel analysis using generalized eigenvectors proves successful.",
keywords = "Brauer character, Markov chain, McKay correspondence, Modular representation, Quantum group, Tensor product",
author = "Georgia Benkart and Persi Diaconis and Liebeck, {Martin W.} and Tiep, {Pham Huu}",
note = "Funding Information: We acknowledge the support of the National Science Foundation under Grant No. DMS-1440140 while in residence at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California, during the Spring 2018 semester. The second author acknowledges the support of the NSF grant DMS-1208775 , and the fourth author acknowledges the support of the NSF grant DMS-1840702 and the Joshua Barlaz Chair in Mathematics. We also thank Phillipe Bougerol, Valentin Buciumas, Daniel Bump, David Craven, Manon deFosseux, Marty Isaacs, Sasha Kleshchev, Gabriel Navarro, Neil O'Connell, and Aner Shalev for helpful discussions. Kay Magaard worked with all of us during our term at MSRI, and we will miss his enthusiasm and insights. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",
year = "2020",
month = nov,
day = "1",
doi = "10.1016/j.jalgebra.2019.10.038",
language = "English (US)",
volume = "561",
pages = "17--83",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}