“Tensor Product Markov Chains”

If G is a finite group, A Markov Chain can be built on the set of ordinary irreducible characters of G by fixing a character and from a given irreducible, tensoring with the fixed character and picking a piece of the tensor product with probability proportional to its multiplicity times dimension. In this talk I will motivate the study of such walks via basic computational group theory (how can we construct the irreducibles of a given finite group), via the McKay correspondence (finite subgroups of SU(2) correspond to A,D,E Dynkin diagrams), via ‘sometimes the walks are interesting’ (Pitman’s 2M-X theorem), via ‘there is a pretty complete theory of such random walks, so sharp rates of convergence can be given’, and via ‘asymptotic group theory'(what does a typical character ‘look like’). In later talks in this series I’ll try to say versions for modular representations and for quantum groups at roots of unity, but this talk will be about the easiest examples. This is joint work with Georgia Benkart, Martin Liebeck and Pham Tiep.

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Quantum Groups Learning SeminarPersi Diaconis (Stanford)

September 26, 2018

12:00 PM - 1:00 PM