Combinatorial, probabilistic and operator problems of asymptotic theory of the representations

I will mention several problems which seems to be central from point of view more that 30 years distance of the theory. Among them:

1. Construction of representations and models of statistical physics;
2. Central (invariant) measures and traces of algebras;
3. Three dimension Young diagram;
4. Continual models and new infinite dimensional groups;
5. Statistics on Young diagrams and partitions.

Лекция прочитана в рамках St. Petersburg School in Probability and Statistical Physics

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