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Mat. Sb., 1989, Volume 180, Number 1, Pages 3–38 (Mi msb1594)  

This article is cited in 12 scientific papers (total in 13 papers)

Hypergeometric functions associated with the Grassmannian $G_{3,6}$

I. M. Gel'fand, M. I. Graev


Abstract: Hypergeometric functions are studied on the variety $G_{3,6}$ of three-dimensional subspaces in $\mathbf C^6$ and on nondegenerate strata in $G_{3,6}$. They are described in the form of power series, systems of differential equations and integrals of Euler type. A connection is established between these functions and some classical hypergeometric functions of one and two variables.
Figures: 1.
Bibliography: 12 titles.

Full text: PDF file (1947 kB)
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English version:
Mathematics of the USSR-Sbornik, 1990, 66:1, 1–40

Bibliographic databases:

UDC: 517.95
MSC: Primary 33A75, 32M10, 22E45; Secondary 32C38, 33A30, 14D05, 32L25, 32C42, 58G07
Received: 09.06.1988

Citation: I. M. Gel'fand, M. I. Graev, “Hypergeometric functions associated with the Grassmannian $G_{3,6}$”, Mat. Sb., 180:1 (1989), 3–38; Math. USSR-Sb., 66:1 (1990), 1–40

Citation in format AMSBIB
\Bibitem{GelGra89}
\by I.~M.~Gel'fand, M.~I.~Graev
\paper Hypergeometric functions associated with the Grassmannian $G_{3,6}$
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 1
\pages 3--38
\mathnet{http://mi.mathnet.ru/msb1594}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=988844}
\zmath{https://zbmath.org/?q=an:0692.33005|0667.33008}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 66
\issue 1
\pages 1--40
\crossref{https://doi.org/10.1070/SM1990v066n01ABEH001931}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990DK06800001}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gelfand I., Grayev M., Retakh V., “Hypergeometrical Functions on Lambda(K)C(N) and the Grassmanian Gk,N and Connections Between Them”, 320, no. 1, 1991, 20–24  isi
    2. Gelfand I., Grayev M., Retakh V., “Reduction Formulas for Hypergeometrical Functions on Grassmanian Gk,N and the Description of Hypergeometrical Functions on Strata of Small Codimension”, 318, no. 4, 1991, 793–797  isi
    3. I. M. Gel'fand, M. I. Graev, V. S. Retakh, “General hypergeometric systems of equations and series of hypergeometric type”, Russian Math. Surveys, 47:4 (1992), 1–88  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Gelfand I., Graev M., “Gg-Functions”, Dokl. Akad. Nauk, 328:6 (1993), 645–648  mathnet  mathscinet  isi
    5. I. M. Pak, A. E. Postnikov, “Transversal Matroids and Strata on Grassmannians”, Funct. Anal. Appl., 29:2 (1995), 140–143  mathnet  crossref  mathscinet  zmath  isi
    6. I. M. Gel'fand, M. I. Graev, “$GG$-functions and their relation to general hypergeometric functions”, Russian Math. Surveys, 52:4 (1997), 639–684  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Gelfand I., Graev M., “Gg-Functions and their Connection with General Hypergeometric Functions”, Dokl. Akad. Nauk, 354:5 (1997), 583–586  mathnet  mathscinet  isi
    8. Gelfand I., Graev M., “Gg Functions and their Relations to General Hypergeometric Functions”, Lett. Math. Phys., 50:1 (1999), 1–27  crossref  mathscinet  isi
    9. A. W. Niukkanen, “Extending the factorization principle to hypergeometric series of general form”, Math. Notes, 67:4 (2000), 487–494  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Niukkanen A., Paramonova O., “Computer Generation of Complicated Transformations and Reduction Formulas for Multiple Hypergeometric Series”, Comput. Phys. Commun., 126:1-2 (2000), 141–148  crossref  mathscinet  zmath  adsnasa  isi
    11. A. W. Niukkanen, O. S. Paramonova, “Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$”, Math. Notes, 71:1 (2002), 80–89  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. A. M. Vershik, I. M. Gel'fand, S. G. Gindikin, A. A. Kirillov, G. L. Litvinov, V. F. Molchanov, Yu. A. Neretin, V. S. Retakh, “Mark Iosifovich Graev (to his 85th brithday)”, Russian Math. Surveys, 63:1 (2008), 173–188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. I. V. Bubyakin, “O stroenii pyatimernykh kompleksov dvumernykh ploskostei v proektivnom prostranstve $P^5$ s edinstvennym torsom”, Matematicheskie zametki SVFU, 24:2 (2017), 3–12  mathnet  crossref  elib
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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