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Finite dimensional representations of sympletic reflection algebras for wreath products

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dc.contributor.advisor Pavel Etingof. en_US Montarani, Silvia en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2008-12-11T16:56:12Z 2008-12-11T16:56:12Z 2008 en_US 2008 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. en_US
dc.description This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. en_US
dc.description Includes bibliographical references (p. 135-137). en_US
dc.description.abstract Symplectic reflection algebras are attached to any finite group G of automorphisms of a symplectic vector space V , and are a multi-parameter deformation of the smash product TV ?G, where TV is the tensor algebra. Their representations have been studied in connection with different subjects, such as symplectic quotient singularities, Hilbert scheme of points in the plane and combinatorics. Let ... SL(2,C) be a finite subgroup, and let Sn be the symmetric group on n letters. We study finite dimensional representations of the wreath product symplectic reflection algebra ... of rank n, attached to the wreath product group ... and to the parameters (k, c), where k is a complex number (occurring only for n > 1), and c a class function on the set of nontrivial elements of ... In particular, we construct, for the first time, families of irreducible finite dimensional modules when ... is not cyclic, n > 1, and (k, c) vary in some linear subspace of the space of parameters. The method is deformation theoretic and uses properties of the Hochschild cohomology of H1,k,c(...), and a Morita equivalence, established by Crawley-Boevey and Holland, between the rank one algebra H1, ... and the deformed preprojective algebra ?Q), where Q is the extended Dynkin quiver attached to ?? via the McKay correspondence. We carry out a similar construction for continuous wreath product symplectic reflection algebras, a generalization to the case when ... SL(2,C) is infinite reductive. This time the main tool is the definition of a continuous analog of the deformed preprojective algebras for the infinite affine Dynkin quivers corresponding to the infinite reductive subgroups of SL(2,C). en_US
dc.description.statementofresponsibility by Silvia Montarani. en_US
dc.format.extent 137 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Finite dimensional representations of sympletic reflection algebras for wreath products en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 261342838 en_US

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