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This article is cited in 3 scientific papers (total in 3 papers)
Rational differential forms on the line and singular vectors in Verma modules over $\widehat{sl}_2$
Vadim Schechtmana, Alexander Varchenkob a Institut de Mathématiques de Toulouse — Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France
b Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA
Abstract:
We construct a monomorphism of the De Rham complex of scalar multivalued meromorphic forms on the projective line, holomorphic on the complement to a finite set of points, to the chain complex of the Lie algebra of $\mathbf{sl}_2$-valued algebraic functions on the same complement with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra $\widehat{sl}_2$. We show that the existence of singular vectors in the Verma modules (the Malikov–Feigin–Fuchs singular vectors) is reflected in the new relations between the cohomology classes of logarithmic differential forms.
Key words and phrases:
Gauss–Manin connection, Malikov–Feigin–Fuchs singular vectors, conformal blocks.
Citation:
Vadim Schechtman, Alexander Varchenko, “Rational differential forms on the line and singular vectors in Verma modules over $\widehat{sl}_2$”, Mosc. Math. J., 17:4 (2017), 787–802
Linking options:
https://www.mathnet.ru/eng/mmj658 https://www.mathnet.ru/eng/mmj/v17/i4/p787
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Abstract page: | 116 | References: | 35 |
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