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Center of infinitesimal Cherednik algebras of $ \mathfrak{gl}_n$


Author: Akaki Tikaradze
Journal: Represent. Theory 14 (2010), 1-8
MSC (2010): Primary 17-XX
DOI: https://doi.org/10.1090/S1088-4165-10-00363-8
Published electronically: January 4, 2010
MathSciNet review: 2577654
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Abstract: We show that the center of an infinitesimal Cherednik algebra of $ \mathfrak{gl}_n$ is isomorphic to the polynomial algebra of $ n$ variables. As consequences of this fact, we show that an analog of Duflo's theorem holds and all objects in the category $ \mathcal{O}$ have finite length.


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Additional Information

Akaki Tikaradze
Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
Email: atikara@utnet.utoledo.edu

DOI: https://doi.org/10.1090/S1088-4165-10-00363-8
Received by editor(s): May 5, 2009
Received by editor(s) in revised form: July 7, 2009
Published electronically: January 4, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.