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Zapiski Nauchnykh Seminarov POMI, 2020, Volume 494, Pages 219–227
(Mi znsl6987)
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Probability measure near the boundary of tensor power decomposition for $\mathfrak{so}_{2n+1}$
A.A. Nazarov, V. L. Chizhikova Department of Physics, St. Petersburg State University, Ulyanovskaya 1, 198504 St. Petersburg, Russia
Abstract:
Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental representation. In this paper we calculate the asymptotics of character measure on representations of $\mathfrak{so}_{2n+1}$ in the regime near the boundary of weight diagram. We find out that it converges to a Poisson-type distribution.
Key words and phrases:
character measure, Lie algebras, Lie groups, irreducible representations, Poisson distribution, tensor power decomposition.
Received: 02.10.2020
Citation:
A.A. Nazarov, V. L. Chizhikova, “Probability measure near the boundary of tensor power decomposition for $\mathfrak{so}_{2n+1}$”, Questions of quantum field theory and statistical physics. Part 27, Zap. Nauchn. Sem. POMI, 494, POMI, St. Petersburg, 2020, 219–227
Linking options:
https://www.mathnet.ru/eng/znsl6987 https://www.mathnet.ru/eng/znsl/v494/p219
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Abstract page: | 87 | Full-text PDF : | 25 | References: | 17 |
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