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 Tr. Mat. Inst. Steklova, 2005, Volume 251, Pages 307–319 (Mi tm55)

Projective Flat Connections on Moduli Spaces of Riemann Surfaces and the Knizhnik–Zamolodchikov Equations

O. K. Sheinman

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus with marked points is developed. Here, the globality means that one uses the Krichever–Novikov algebras of gauge and conformal symmetries (i.e., of global symmetries) instead of the loop and Virasoro algebras, which are local in this context. A thorough account of the global approach with all necessary details from the theory of Krichever–Novikov algebras and their representations was given by the author earlier (Usp. Mat. Nauk, 1999, vol. 54, no. 1; 2004, vol. 59, no. 4). This paper focuses on the geometric ideas that underlie our construction of conformal blocks. We prove the invariance of these blocks with respect to the (generalized) Knizhnik–Zamolodchikov connection and the projective flatness of this connection.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 251, 293–304

Bibliographic databases:
UDC: 512.554.32

Citation: O. K. Sheinman, “Projective Flat Connections on Moduli Spaces of Riemann Surfaces and the Knizhnik–Zamolodchikov Equations”, Nonlinear dynamics, Collected papers, Tr. Mat. Inst. Steklova, 251, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 307–319; Proc. Steklov Inst. Math., 251 (2005), 293–304

Citation in format AMSBIB
\Bibitem{She05} \by O.~K.~Sheinman \paper Projective Flat Connections on Moduli Spaces of Riemann Surfaces and the Knizhnik--Zamolodchikov Equations \inbook Nonlinear dynamics \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2005 \vol 251 \pages 307--319 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm55} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2234387} \zmath{https://zbmath.org/?q=an:1119.32007} \transl \jour Proc. Steklov Inst. Math. \yr 2005 \vol 251 \pages 293--304 

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This publication is cited in the following articles:
1. 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
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