ART is more or less a new branch of representation theory, in between Analysis, Combinatorics, Probability and Representation theory itself. The main objects are behavior of representations of the groups of large rank and representations of limit groups. I will give a short survey and formulate several problems related to the irreducible and admissible representations of $S_{\infty}$, and markov measures on infinite Young tableaux. Indeed all these questions are intimately connected to new questions about representations of finite groups.

Lecture #12705

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