Quantized multiplicative quiver varieties and actions of higher genus braid groups
Name
767740932-MIT.pdf
Description
Full printable version
Size
4.85 MB
Format
Adobe PDF
Checksum (MD5)
fa833db7ac169a1f0212a3a358c7a184
Author(s)
Jordan, David Andrew
Advisor(s)
Pavel Etingof.
Alternative Title
Quantized multiplicative quiver varieties
Date Issued
2011
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, a new class of algebras called quantized multiplicative quiver varieties A (Q), is constructed, depending upon a quiver Q, its dimension vector d, and a certain "moment map" parameter . The algebras Ad(Q) are obtained via quantum Hamiltonian reduction of another algebra D,(Matd(Q)) relative to a quantum moment map pq, both of which are also constructed herein. The algebras Dq(Matd(Q)) and A (Q) bear relations to many constructions in representation theory, some of which are spelled out herein, and many more whose precise formulation remains conjectural. When Q consists of a single vertex of dimension N with a single loop, the algebra Dq(MatA(Q)) is isomorphic to the algebra of quantum differential operators on G = GLN. In this case, for any n E Z>o, we construct a functor from the category of Dq-modules to representations of the type A double affine Hecke algebra of rank n. This functor is an instance of a more general construction which may be applied to any quasi-triangular Hopf algebra H, and yields representations of the elliptic braid group of rank n.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 109-112).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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