On trigonometric and elliptic Cherednik algebras
Name
727163751-MIT.pdf
Description
Full printable version
Size
3.58 MB
Format
Adobe PDF
Checksum (MD5)
9a65d1d69923b3a4a8dd176e7aab5600
Author(s)
Ma, Xiaoguang, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Pavel Etingof.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 87-90).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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