Unitary representations of rational Cherednik algebras and Hecke algebras
Name
727146279-MIT.pdf
Description
Full printable version
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1.92 MB
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Author(s)
Stoica, Emanuel (Emanuel I.)
Advisor(s)
Pavel Etingof.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
We begin the study of unitary representations in the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection groups and provide a complete classification in the case of the symmetric group. We conclude that the KZ functor defined in [16] preserves unitarity in type A. Finally, we formulate a few conjectures concerning the classification of unitary representations for other types and the preservation of unitarity by the KZ functor and the restriction functors defined in [2].
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 49-50).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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