On trigonometric and elliptic Cherednik algebras

• Main Author: Ma, Xiaoguang, Ph. D. Massachusetts Institute of Technology
• Other Authors: Pavel Etingof.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2011
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/64611

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. === Cataloged from PDF version of thesis. === Includes bibliographical references (p. 87-90). === 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. === by Xiaoguang Ma. === Ph.D.