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Zapiski Nauchnykh Seminarov POMI, 2020, Volume 494, Pages 219–227 (Mi znsl6987)  

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
References:
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
Document Type: Article
Language: English
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
Citation in format AMSBIB
\Bibitem{NazChi20}
\by A.A.~Nazarov, V.~L.~Chizhikova
\paper Probability measure near the boundary of tensor power decomposition for $\mathfrak{so}_{2n+1}$
\inbook Questions of quantum field theory and statistical physics. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2020
\vol 494
\pages 219--227
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6987}
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  • https://www.mathnet.ru/eng/znsl/v494/p219
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