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Russian Mathematical Surveys, 2004, Volume 59, Issue 4, Pages 737–770
DOI: https://doi.org/10.1070/RM2004v059n04ABEH000760
(Mi rm760)
 

This article is cited in 20 scientific papers (total in 20 papers)

Knizhnik–Zamolodchikov equations for positive genus and Krichever–Novikov algebras

M. Schlichenmaiera, O. K. Sheinmanbc

a University of Luxembourg
b Steklov Mathematical Institute, Russian Academy of Sciences
c Independent University of Moscow
References:
Abstract: In this paper a global operator approach to the Wess–Zumino–Witten–Novikov theory for compact Riemann surfaces of arbitrary genus with marked points is developed. The term ‘global’ here means that Krichever–Novikov algebras of gauge and conformal symmetries (that is, algebras of global symmetries) are used instead of loop algebras and Virasoro algebras (which are local in this context). The basic elements of this global approach are described in a previous paper of the authors (Russ. Math. Surveys 54:1 (1999)). The present paper gives a construction of the conformal blocks and of a projectively flat connection on the bundle formed by them.
Received: 15.03.2004
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 4(358), Pages 147–180
DOI: https://doi.org/10.4213/rm760
Bibliographic databases:
Document Type: Article
UDC: 517.774
MSC: Primary 17B66, 17B67, 81R10; Secondary 14H15, 14H55, 30F30
Language: English
Original paper language: Russian
Citation: M. Schlichenmaier, O. K. Sheinman, “Knizhnik–Zamolodchikov equations for positive genus and Krichever–Novikov algebras”, Uspekhi Mat. Nauk, 59:4(358) (2004), 147–180; Russian Math. Surveys, 59:4 (2004), 737–770
Citation in format AMSBIB
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\by M.~Schlichenmaier, O.~K.~Sheinman
\paper Knizhnik--Zamolodchikov equations for positive genus and Krichever--Novikov algebras
\jour Uspekhi Mat. Nauk
\yr 2004
\vol 59
\issue 4(358)
\pages 147--180
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\transl
\jour Russian Math. Surveys
\yr 2004
\vol 59
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\pages 737--770
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-11144281296}
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  • https://doi.org/10.1070/RM2004v059n04ABEH000760
  • https://www.mathnet.ru/eng/rm/v59/i4/p147
    Cycle of papers
    This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Успехи математических наук Russian Mathematical Surveys
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    Abstract page:648
    Russian version PDF:284
    English version PDF:21
    References:77
    First page:1
     
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