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Izv. RAN. Ser. Mat., 1993, Volume 57, Issue 6, Pages 29–51 (Mi izv824)  

This article is cited in 7 scientific papers (total in 7 papers)

The infinite-demensional $p$-adic symplectic group

E. I. Zelenov


Abstract: An analogue of the Fock representation is constructed for the infinite-dimensional $p$-adic Heisenberg group.The restricted symplectic group is defined for an infinite-dimensional symplectic space over the field $\mathbf Q_p$of $p$-adic numbers. For the restricted symplectic group a projective representation is constructed that is compatible with the representation of the Heisenberg group, and an expression for the cocycle of this representation is given in terms of the $p$-adic Maslov index. It is proved that the extension corresponding to this cocycle reduces to a $\mathbf Z_2$-extension.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1994, 43:3, 421–441

Bibliographic databases:

UDC: 513.015.7
MSC: Primary 22E70, 81R10; Secondary 81S05
Received: 29.06.1992

Citation: E. I. Zelenov, “The infinite-demensional $p$-adic symplectic group”, Izv. RAN. Ser. Mat., 57:6 (1993), 29–51; Russian Acad. Sci. Izv. Math., 43:3 (1994), 421–441

Citation in format AMSBIB
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\by E.~I.~Zelenov
\paper The infinite-demensional $p$-adic symplectic group
\jour Izv. RAN. Ser. Mat.
\yr 1993
\vol 57
\issue 6
\pages 29--51
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1256565}
\zmath{https://zbmath.org/?q=an:0836.22025}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..43..421Z}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 43
\issue 3
\pages 421--441
\crossref{https://doi.org/10.1070/IM1994v043n03ABEH001573}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994QK21500002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Youngho JANG, “Non-Archimedean quantum mechanics”, Tohoku Math Publ, 10:10 (1998), 1  crossref  mathscinet  zmath
    2. Taekyun Kim, Dal-Won Park, Seog-Hoon Rim, J Phys A Math Gen, 34:37 (2001), 7633  crossref  mathscinet  zmath  isi
    3. Proc. Steklov Inst. Math., 245 (2004), 258–265  mathnet  mathscinet  zmath
    4. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “On p-adic mathematical physics”, P-Adic Num Ultrametr Anal Appl, 1:1 (2009), 1  crossref  mathscinet
    5. Yu. A. Neretin, “Hua measures on the space of $p$-adic matrices and inverse limits of Grassmannians”, Izv. Math., 77:5 (2013), 941–953  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. E. I. Zelenov, “$p$-Adic model of quantum mechanics and quantum channels”, Proc. Steklov Inst. Math., 285 (2014), 132–144  mathnet  crossref  crossref  isi  elib
    7. Zuniga-Galindo W.A., “Non-Archimedean White Noise, Pseudodifferential Stochastic Equations, and Massive Euclidean Fields”, J. Fourier Anal. Appl., 23:2 (2017), 288–323  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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