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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 240, Pages 67–77 (Mi znsl466)  
Macdonald identities and multidimensional theta-functions

M. A. Vsemirnov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (204 kB)
Abstract: A new proof of the combinatorial Macdonald identities is presented. It is shown that one may regard these identities as decomposition of multidimensional theta-functions into infinite products. The proof is pased on some analytical properties of theta-functions. It is discussed briefly now one may modify the proof in order to replace analytical reasonings by the formal ones involving only operations with formal series.
Received: 21.11.1996
English version:
Journal of Mathematical Sciences (New York), 1999, Volume 96, Issue 5, Pages 3486–3492
DOI: https://doi.org/10.1007/BF02175826
Bibliographic databases:
UDC: 519.117
Language: Russian
Citation: M. A. Vsemirnov, “Macdonald identities and multidimensional theta-functions”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Zap. Nauchn. Sem. POMI, 240, POMI, St. Petersburg, 1997, 67–77; J. Math. Sci. (New York), 96:5 (1999), 3486–3492
Citation in format AMSBIB
\Bibitem{Vse97}
\by M.~A.~Vsemirnov
\paper Macdonald identities and multidimensional theta-functions
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~II
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 240
\pages 67--77
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl466}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1691638}
\zmath{https://zbmath.org/?q=an:0941.11019}
\transl
\jour J. Math. Sci. (New York)
\yr 1999
\vol 96
\issue 5
\pages 3486--3492
\crossref{https://doi.org/10.1007/BF02175826}
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