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. Surveys54:1 (1999)). The present paper gives a construction of the conformal blocks and of a projectively flat connection on the bundle formed by them.
Citation:
M. Schlichenmaier, O. K. Sheinman, “Knizhnik–Zamolodchikov equations for positive genus and Krichever–Novikov algebras”, Russian Math. Surveys, 59:4 (2004), 737–770
This publication is cited in the following 20 articles:
O. K. Sheinman, “Quantization of integrable systems with spectral parameter on a Riemann surface”, Dokl. Math., 102:3 (2020), 524–527
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Schlichenmaier M., “N -point Virasoro algebras are multipoint Krichever–Novikov-type algebras”, Commun. Algebr., 45:2 (2017), 776–821
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Cox B. Guo X. Lu R. Zhao K., “N-Point Virasoro Algebras and Their Modules of Densities”, Commun. Contemp. Math., 16:3 (2014), 1350047
Martin Schlichenmaier, Harmonic and Complex Analysis and its Applications, 2014, 325
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M. Schlichenmaier, O. K. Sheinman, “Central extensions of Lax operator algebras”, Russian Math. Surveys, 63:4 (2008), 727–766
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Fialowski A., Schlichenmaier M., “Global geometric deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebras”, Internat. J. Theoret. Phys., 46:11 (2007), 2708–2724
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
Schlichenmaier M., “Higher Genus Affine Lie Algebras of Krichever - Novikov Type”, Difference Equations, Special Functions and Orthogonal Polynomials, 2007, 589–599
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
Martin Schlichenmaier, Theoretical and Mathematical Physics, An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces, 2007, 103
Fialowski A., Schlichenmaier M., “Global geometric deformations of current algebras as Krichever-Novikov type algebras”, Comm. Math. Phys., 260:3 (2005), 579–612
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
Sheinman O.K., “Krichever-Novikov algebras and their representations”, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics Series, 391, 2005, 313–321
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