On trigonometric and elliptic Cherednik algebras

In this thesis, we study the trigonometric and elliptic Cherednik algebras. In the first part, we give a Lie-theoretic construction of the trigonometric Cherednik algebras of type BC,. We construct a functor from the category of Harish- Chandra modules of the symmetric pair of type AIII to the category of representations of the degenerate affine and double affine Hecke algebra of type BC. We also study the images of some D-modules and the principal series modules. In the second part, we define the elliptic Dunkl operators on an abelian variety with a finite group action. Using these elliptic Dunkl operators, we construct a new family of quantum integrable systems.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Ma, Xiaoguang, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Pavel Etingof.

• Mathematics.

Statement 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/64611

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/64611