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Mosc. Math. J., 2001, Volume 1, Number 4, Pages 605–628 (Mi mmj40)  

This article is cited in 8 scientific papers (total in 8 papers)

Second order Casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$

O. K. Sheinmanab

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

Abstract: The second order casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$ are described. More general operators which we call semi-casimirs are introduced. It is proven that the semi-casimirs induce well-defined operators on conformal blocks and, for a certain moduli space of Riemann surfaces with two marked points and fixed jets of local coordinates, there is a natural projection of its tangent space onto the space of these operators.

Key words and phrases: Infinite-dimensional Lie algebras, Riemann surfaces, current algebras, central extensions, highest weight representations, wedge representations, Casimir operators, moduli spaces, conformal blocks.

DOI: https://doi.org/10.17323/1609-4514-2001-1-4-605-628

Full text: http://www.ams.org/.../abst1-4-2001.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 17B66, 17B67, 14H10, 14H15, 17B90, 30F30, 14H55, 81R10, 81T40
Language:

Citation: 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

Citation in format AMSBIB
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\by O.~K.~Sheinman
\paper Second order Casimirs for the affine Krichever--Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$
\jour Mosc. Math.~J.
\yr 2001
\vol 1
\issue 4
\pages 605--628
\mathnet{http://mi.mathnet.ru/mmj40}
\crossref{https://doi.org/10.17323/1609-4514-2001-1-4-605-628}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1901079}
\zmath{https://zbmath.org/?q=an:1123.17300}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208587600009}


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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. M. Schlichenmaier, “Higher genus affine algebras of Krichever–Novikov type”, Mosc. Math. J., 3:4 (2003), 1395–1427  mathnet  mathscinet  zmath
    2. Schlichenmaier M., “Local cocycles and central extensions for multipoint algebras of Krichever-Novikov type”, J. Reine Angew. Math., 559 (2003), 53–94  crossref  mathscinet  zmath  isi
    3. 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
    4. 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
    5. 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
    6. 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
    7. Cox B. Jurisich E., “Realizations of the Three-Point Lie Algebra Sl(2, R) Circle Plus (Omega(R)/Dr)”, Pac. J. Math., 270:1 (2014), 27–47  crossref  mathscinet  isi  elib
    8. Schlichenmaier M., “Krichever-Novikov Type Algebras: Theory and Applications”, Krichever-Novikov Type Algebras: Theory and Applications, Degruyter Studies in Mathematics, 53, Walter de Gruyter Gmbh, 2014, 1–360  crossref  mathscinet  isi
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