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 Mosc. Math. J., 2010, Volume 10, Number 2, Pages 469–475 (Mi mmj388)

A Selberg integral type formula for an $\mathfrak{sl}_2$ one-dimensional space of conformal blocks

A. Varchenko

Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

Abstract: For distinct complex numbers $z_1,…,z_{2N}$, we give a polynomial $P(y_1,…,y_{2N})$ in the variables $y_1,…,y_{2N}$ which is homogeneous of degree $N$, linear with respect to each variable, $\mathfrak{sl}_2$-invariant with respect to a natural $\mathfrak{sl}_2$-action, and is of order $N-1$ at $(y_1,…,y_{2N})=(z_1,…,z_{2N})$.
We give also a Selberg integral type formula for the associated one-dimensional space of conformal blocks.

Key words and phrases: conformal blocks, invariant polynomials.

DOI: https://doi.org/10.17323/1609-4514-2010-10-2-469-475

Full text: http://www.ams.org/.../abst10-2-2010.html
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Bibliographic databases:

MSC: Primary 81T40, 33C70; Secondary 32S40, 52B30
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Citation: A. Varchenko, “A Selberg integral type formula for an $\mathfrak{sl}_2$ one-dimensional space of conformal blocks”, Mosc. Math. J., 10:2 (2010), 469–475

Citation in format AMSBIB
\Bibitem{Var10} \by A.~Varchenko \paper A Selberg integral type formula for an $\mathfrak{sl}_2$ one-dimensional space of conformal blocks \jour Mosc. Math.~J. \yr 2010 \vol 10 \issue 2 \pages 469--475 \mathnet{http://mi.mathnet.ru/mmj388} \crossref{https://doi.org/10.17323/1609-4514-2010-10-2-469-475} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2722806} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279342400009} 

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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. A. N. Varchenko, R. Rimányi, V. O. Tarasov, V. V. Schechtman, “Cohomology of a flag variety as a Bethe algebra”, Funct. Anal. Appl., 45:4 (2011), 252–264
2. Rimanyi R., Tarasov V., Varchenko A., Zinn-Justin P., “Extended Joseph Polynomials, Quantized Conformal Blocks, and a Q-Selberg Type Integral”, J. Geom. Phys., 62:11 (2012), 2188–2207
3. Gorbounov V. Rimanyi R. Tarasov V. Varchenko A., “Quantum Cohomology of the Cotangent Bundle of a Flag Variety as a Yangian Bethe Algebra”, J. Geom. Phys., 74 (2013), 56–86
4. Rimanyi R. Tarasov V. Varchenko A., “Cohomology Classes of Conormal Bundles of Schubert Varieties and Yangian Weight Functions”, Math. Z., 277:3-4 (2014), 1085–1104