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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 487, Pages 40–52 (Mi znsl6900)  
Completeness of the $3j$-symbols for $SL(2,\mathbb C)$ group

N. M. Belousov, S. È. Derkachev

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
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Abstract: The main formulas for the unitary series of representations of the group $SL(2,\mathbb C)$ are given, and the decomposition of a tensor product of two representations into irreducible is considered. A simple proof of completeness of the $3j$-symbols is given.
Key words and phrases: representation theory of SL(2,C) group, 3j-symbols, completeness relation, unitary principal series representations, decomposition of a tensor product of representations.
Funding agency Grant number
Russian Science Foundation 19-11-00131
Received: 26.11.2019
Document Type: Article
UDC: 517.9
Language: Russian
Citation: N. M. Belousov, S. È. Derkachev, “Completeness of the $3j$-symbols for $SL(2,\mathbb C)$ group”, Questions of quantum field theory and statistical physics. Part 26, Zap. Nauchn. Sem. POMI, 487, POMI, St. Petersburg, 2019, 40–52
Citation in format AMSBIB
\Bibitem{BelDer19}
\by N.~M.~Belousov, S.~\`E.~Derkachev
\paper Completeness of the $3j$-symbols for $SL(2,\mathbb C)$ group
\inbook Questions of quantum field theory and statistical physics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 487
\pages 40--52
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6900}
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