Center of infinitesimal Cherednik algebras of $\mathfrak {gl}_n$
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- by Akaki Tikaradze
- Represent. Theory 14 (2010), 1-8
- DOI: https://doi.org/10.1090/S1088-4165-10-00363-8
- Published electronically: January 4, 2010
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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.References
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Bibliographic Information
- Akaki Tikaradze
- Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
- MR Author ID: 676866
- Email: atikara@utnet.utoledo.edu
- Received by editor(s): May 5, 2009
- Received by editor(s) in revised form: July 7, 2009
- Published electronically: January 4, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory 14 (2010), 1-8
- MSC (2010): Primary 17-XX
- DOI: https://doi.org/10.1090/S1088-4165-10-00363-8
- MathSciNet review: 2577654