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Mat. Sb., 1989, Volume 180, Number 5, Pages 635–657 (Mi msb1625)  

This article is cited in 17 scientific papers (total in 17 papers)

Holomorphic extensions of representations of the group of the diffeomorphisms of the circle

Yu. A. Neretin


Abstract: This paper gives the construction of a semigroup $\Gamma$ which could be thought of as the complexincation of the group $\operatorname{Diff}$ of analytic diffeomorphisms of the circle, and it is shown that any unitary projective representation of $\operatorname{Diff}$ with highest weight has a holomorphic extension to $\Gamma$. For this, $\Gamma$ is embedded in the semigroup of “endomorphisms of canonical commutation relations” (this is a certain part of the Lagrange Grassmannian in complex symplectic Hilbert space).
Bibliography: 25 titles.

Full text: PDF file (1356 kB)
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English version:
Mathematics of the USSR-Sbornik, 1990, 67:1, 75–97

Bibliographic databases:

UDC: 517.9
MSC: 22E65, 17B65
Received: 18.01.1988

Citation: Yu. A. Neretin, “Holomorphic extensions of representations of the group of the diffeomorphisms of the circle”, Mat. Sb., 180:5 (1989), 635–657; Math. USSR-Sb., 67:1 (1990), 75–97

Citation in format AMSBIB
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\by Yu.~A.~Neretin
\paper Holomorphic extensions of representations of the~group of the~diffeomorphisms of the~circle
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 5
\pages 635--657
\mathnet{http://mi.mathnet.ru/msb1625}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1007467}
\zmath{https://zbmath.org/?q=an:0696.58010}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 1
\pages 75--97
\crossref{https://doi.org/10.1070/SM1990v067n01ABEH001321}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990ED88000005}


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  • http://mi.mathnet.ru/eng/msb/v180/i5/p635

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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. Yu. A. Neretin, “A semigroup of operators in the boson fock space”, Funct. Anal. Appl., 24:2 (1990), 135–144  mathnet  crossref  mathscinet  zmath  isi
    2. Neretin I., “On Operators Connecting Holomorphic Representations of Different Groups”, 312, no. 6, 1990, 1318–1321  mathscinet  zmath  isi
    3. Yu. A. Neretin, “Categories of bistochastic measures, and representations of some infinite-dimensional groups”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 197–219  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Yu. A. Neretin, “Universal completions of complex classical groups”, Funct. Anal. Appl., 26:4 (1992), 254–265  mathnet  crossref  mathscinet  zmath  isi
    5. D. V. Yur'ev, “Quantum projective field theory: Quantum-field analogs of the Euler–Arnol'd equations in projective $G$ multiplets”, Theoret. and Math. Phys., 98:2 (1994), 147–161  mathnet  crossref  mathscinet  zmath  isi
    6. B. Julia, H. Nicolai, “Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton”, Nuclear Physics B, 482:1-2 (1996), 431  crossref
    7. Yu. A. Neretin, “On the correspondence between boson Fock space and the $L^2$ space with respect to Poisson measure”, Sb. Math., 188:11 (1997), 1587–1616  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Yu. A. Neretin, “Supercomplete Bases in the Space of Symmetric Functions”, Funct. Anal. Appl., 32:1 (1998), 10–22  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Helene Airault, “Affine coordinates and Virasoro unitarizing measures”, Journal de Mathématiques Pures et Appliquées, 82:4 (2003), 425  crossref  elib
    10. Helene Airault, Vladimir Bogachev, “Realization of Virasoro unitarizing measures on the set of Jordan curves”, Comptes Rendus Mathematique, 336:5 (2003), 429  crossref
    11. Yu. A. Neretin, “$K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric”, Funct. Anal. Appl., 41:4 (2007), 295–302  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Richard Blute, Prakash Panangaden, Dorette Pronk, “Conformal Field Theory as a Nuclear Functor”, Electronic Notes in Theoretical Computer Science, 172 (2007), 101  crossref
    13. Helene Airault, Yuri A. Neretin, “On the action of Virasoro algebra on the space of univalent functions”, Bulletin des Sciences Mathématiques, 132:1 (2008), 27  crossref  elib
    14. Theodore Erler, Martin Schnabl, “A simple analytic solution for Tachyon condensation”, J. High Energy Phys, 2009:10 (2009), 066  crossref
    15. Neretin Yu.A., “Ramified Integrals, Casselman Phenomenon, and Holomorphic Continuations of Group Representations”, Analysis and Mathematical Physics, Trends in Mathematics, eds. Gustafsson B., Vasilev A., Birkhauser Boston, 2009, 427–439  crossref  mathscinet  isi
    16. KARL-HERMANN NEEB, “SEMIBOUNDED REPRESENTATIONS AND INVARIANT CONES IN INFINITE DIMENSIONAL Lie ALGEBRAS”, Confluentes Math, 02:01 (2010), 37  crossref
    17. Yu. A. Neretin, “Infinite symmetric groups and combinatorial constructions of topological field theory type”, Russian Math. Surveys, 70:4 (2015), 715–773  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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