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Creators/Authors contains: "Slinkin, Alexey"

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  1. ; (, Arnold Mathematical Journal)
    null (Ed.)
    We consider the KZ differential equations over C in the case, when the hypergeometric solutions are one-dimensional integrals.We also consider the same differential equations over a finite field F_p. We study the space of polynomial solutions of these differential equations over F_p, constructed in a previous work by Schechtman and the second author. Using Hasse–Witt matrices, we identify the space of these polynomial solutions over F_p with the space dual to a certain subspace of regular differentials on an associated curve. We also relate these polynomial solutions over F_p and the hypergeometric solutions over C. 
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  2. ; (, Symmetry integrability and geometry methods and applications)
    We consider two complexes. The first complex is the twisted de Rham complex of scalar meromorphic differential forms on projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of sl2-valued algebraic functions on the same complement, with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra sl2^. In [Schechtman V., Varchenko A., Mosc. Math. J. 17 (2017), 787-802] a construction of a monomorphism of the first complex to the second was suggested and it was indicated that under this monomorphism the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the relations between the cohomology classes of the de Rham complex. In this paper we prove these results. △ Less 
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