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Comment: Correction of reference of Thm. 9.12 stating an equivalence of categories between modules over the rational Cherednik algebra and its spherical subalgebra
Comment: 9 pages,amstex,talk given by P.Maslanka on "IV Colloqium on Quantum Groups and Integrable Models ",Praque'95
Comment: LaTeX, 9 pages. Submitted for the Proceedings of the 4th International Colloquium ``Quantum Groups and Integrable Systems,'' Prague, 22-24 June 1995
Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integers powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P.Slightly generalizing [Hashimoto-Hayashi,Tohoku Math.Tohoku Math.J. 44(1992)],we define a multiparameter deformation $L_{\l/\mu}V_P$ of the classical skew Schur module.In case R is a field and q is not a root of 1, arguments like those given in [H-H] show that $L_{\l/\mu}V_P$ is irreducible and its decomposition into irreducibles is $\sum_\nu c(\l/\mu;\nu)L_\nu V_P$ where the coefficients are the usual Littlewood-Richardson ones. When R is any ring and q is allowed to be a root of 1, we construct a filtration of $L_{\l/\mu}V_P$ as an SE(q,P)-comodule, such that its associated graded object is precisely $\sum_\nu c(\l...
We show that the stable cohomology of the algebraic polyvector fields on R^n, with values in the adjoint representation is (up to some known classes) the symmetric product space on the cohomology of M. Kontsevich's graph complex.
Comment: 50 pages, typos corrected
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