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Screenings and a universal Lie-de Rham cocycle

Victor Ginzburg·Vadim Schechtman
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Abstract

Feigin and Fuchs have given a well-known construction of intertwining operators between "Fock-type" modules over the Virasoro algebra. The intertwiners are obtained via contour integration of certain "screening operators" over top homology classes of a configuration space. The main observation of the present paper is that the screening operators contain more information. Specifically, at the chain level, the screening operators provide a certain canonical cocycle of the Virasoro (resp. affine Kac-Moody) algebra with coefficients in the de Rham complex of an operator-valued local system on the configuration space. This way we obtain canonical morphisms from higher homology groups of the above local systems to appropriate higher Ext-groups between the Fock space representations. Our construction is motivated by, and in a special case reduces to the construction of Bowknegt et al, see [BMP1], [BMP2].

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Victor Ginzburg, Vadim Schechtman. 1997-09-15. Screenings and a universal Lie-de Rham cocycle. https://arxiv.org/abs/q-alg/9704014

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