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Funktsional. Anal. i Prilozhen., 2001, Volume 35, Issue 3, Pages 60–72 (Mi faa259)  

This article is cited in 10 scientific papers (total in 10 papers)

The Fermion Model of Representations of Affine Krichever–Novikov Algebras

O. K. Sheinmanab

a Independent University of Moscow
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: To a generic holomorphic vector bundle on an algebraic curve and an irreducible finite-dimensional representation of a semisimple Lie algebra, we assign a representation of the corresponding affine Krichever–Novikov algebra in the space of semi-infinite exterior forms. It is shown that equivalent pairs of data give rise to equivalent representations and vice versa.

DOI: https://doi.org/10.4213/faa259

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English version:
Functional Analysis and Its Applications, 2001, 35:3, 209–219

Bibliographic databases:

UDC: 517.9
Received: 11.05.2000

Citation: O. K. Sheinman, “The Fermion Model of Representations of Affine Krichever–Novikov Algebras”, Funktsional. Anal. i Prilozhen., 35:3 (2001), 60–72; Funct. Anal. Appl., 35:3 (2001), 209–219

Citation in format AMSBIB
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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. O. K. Sheinman, “Second-order Casimir operators for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$”, Russian Math. Surveys, 56:5 (2001), 986–987  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. O. K. Sheinman, “Second order Casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$”, Mosc. Math. J., 1:4 (2001), 605–628  mathnet  mathscinet  zmath
    3. O. K. Sheinman, “Krichever–Novikov algebras and self-duality equations on Riemann surfaces”, Russian Math. Surveys, 56:1 (2001), 176–178  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. M. Schlichenmaier, “Higher genus affine algebras of Krichever–Novikov type”, Mosc. Math. J., 3:4 (2003), 1395–1427  mathnet  mathscinet  zmath
    5. M. Schlichenmaier, O. K. Sheinman, “Knizhnik–Zamolodchikov equations for positive genus and Krichever–Novikov algebras”, Russian Math. Surveys, 59:4 (2004), 737–770  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. O. K. Sheinman, “Projective Flat Connections on Moduli Spaces of Riemann Surfaces and the Knizhnik–Zamolodchikov Equations”, Proc. Steklov Inst. Math., 251 (2005), 293–304  mathnet  mathscinet  zmath
    7. O. K. Sheinman, “Highest weight representations of Krichever–Novikov algebras and integrable systems”, Russian Math. Surveys, 60:2 (2005), 370–372  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Sheinman O.K., “Krichever-Novikov algebras and their representations”, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics Series, 391, 2005, 313–321  crossref  mathscinet  zmath  isi
    9. O. K. Sheinman, “Krichever–Novikov Algebras, their Representations and Applications in Geometry and Mathematical Physics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S85–S161  mathnet  crossref  crossref  zmath
    10. Schlichenmaier M., “A global operator approach to Wess-Zumino-Novikov-Witten models”, XXVI Workshop on Geometrical Methods in Physics, AIP Conference Proceedings, 956, 2007, 107–119  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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