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This article is cited in 2 scientific papers (total in 2 papers)
Conformal blocks and equivariant cohomology
Richárd Rimányia, Vadim Schechtmanb, Alexander Varchenkoa a Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
b Institute de Mathématique de Toulouse, Univesité
Paul Sabatier, Toulouse, France
Abstract:
In this paper we show that the conformal blocks constructed in the previous article by the first and the third author may be described as certain integrals in equivariant cohomology. When the bundles of conformal blocks have rank one, this construction may be compared with the old integral formulas of the second and the third author. The proportionality coefficients are some Selberg type integrals which are computed. Finally, a geometric construction of the tensor products of vector representations of the Lie algebra $\mathfrak{gl}(m)$ is proposed.
Key words and phrases:
Wess–Zumino–Witten model, Knizhnik–Zamolodchikov equations, equivariant cohomology, Selberg integrals, Kac–Moody Lie algebras.
Received: September 3, 2010
Citation:
Richárd Rimányi, Vadim Schechtman, Alexander Varchenko, “Conformal blocks and equivariant cohomology”, Mosc. Math. J., 11:3 (2011), 561–581
Linking options:
https://www.mathnet.ru/eng/mmj433 https://www.mathnet.ru/eng/mmj/v11/i3/p561
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Abstract page: | 243 | References: | 43 |
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