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Zapiski Nauchnykh Seminarov LOMI, 1984, Volume 133, Pages 258–276 (Mi znsl4423)  

This article is cited in 4 scientific papers (total in 4 papers)

Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions

L. A. Takhtadzhyan
Full-text PDF (845 kB) Citations (4)
Abstract: The matrix analogues of the Weierstrass zeta and sigma functions are introduced and studied. It is proved in the case of $\mathbb Z_n\times\mathbb Z_n$ symmetry that the classical $r$-matrix coincides with the matrix zeta function and that the quantum $R$-matrix can be represented as the ratio of matrix sigma functions. The obtained formulae are interpreted as the result of averaging over the lattice in $\mathbb C$.
Bibliographic databases:
Document Type: Article
UDC: 517.43+519.46
Language: Russian
Citation: L. A. Takhtadzhyan, “Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions”, Differential geometry, Lie groups and mechanics. Part VI, Zap. Nauchn. Sem. LOMI, 133, "Nauka", Leningrad. Otdel., Leningrad, 1984, 258–276
Citation in format AMSBIB
\Bibitem{Tak84}
\by L.~A.~Takhtadzhyan
\paper Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions
\inbook Differential geometry, Lie groups and mechanics. Part~VI
\serial Zap. Nauchn. Sem. LOMI
\yr 1984
\vol 133
\pages 258--276
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4423}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=742162}
\zmath{https://zbmath.org/?q=an:0542.15003}
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  • https://www.mathnet.ru/eng/znsl/v133/p258
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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