|
Center of infinitesimal Cherednik algebras of 
Author(s):
Akaki
Tikaradze
Journal:
Represent. Theory
14
(2010),
1-8.
MSC (2010):
Primary 17-XX
Posted:
January 4, 2010
MathSciNet review:
2577654
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that the center of an infinitesimal Cherednik algebra of  is isomorphic to the polynomial algebra of  variables. As consequences of this fact, we show that an analog of Duflo's theorem holds and all objects in the category  have finite length.
References:
-
- [BC]
- K. Brown and K. Changtong, Symplectic reflection algebras in positive characteristic, arxiv:0709.2338 (2007).
- [BG]
- K. Brown and I. Goodearl, Homological aspects of Noetherian PI Hopf algebras and irreducible modules of maximal dimension, Journal of Algebra 198 (1997), 240-265. MR 1482982 (99c:16036)
- [EG]
- P. Etingof and V. Ginzburg, Symplectic reflection algebras and Calogero-Moser spaces and deformed Harish-Chandra homomorphism, Inventiones Math. 147 (2002), no. 2, 243-348. MR 1881922 (2003b:16021)
- [EGG]
- P. Etingof, W.L. Gan, and V. Ginzburg, Continuous Hecke algebras, Transform. Groups 10 (2005), no. 3-4, 423-447. MR 2183119 (2006h:20006)
- [G]
- V. Ginzburg, On primitive ideals, Selecta Math. 9 (2003), 379-407. MR 2006573 (2005f:16039)
- [P]
- D. Panyushev, On the coadjoint representation of
 -contractions of reductive Lie algebras, Adv. Math. 213 (2007), no. 1, 380-404. MR 2331248 (2008f:17010) - [KT]
- A. Khare and A. Tikaradze, Center and representations of infinitesimal Hecke algebras of
 , arxiv:0807.4776 (2008). - [R1]
- M. Rais, La représentation coadjointe du groupe affine, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 1, xi, 207-237 MR 500922 (81c:17017)
- [R2]
- M. Rais, Les invariants polynômes de la représentation coadjointe de groupes inhomogénes, arxiv:0903.5146 (2009).
- [S]
- S. Smith, A class of algebras similar to the enveloping algebra of sl(2), Trans. Amer. Math. Soc. 322 (1990), no. 1, 285-314. MR 972706 (91b:17013)
- [T]
- A. Tikaradze, Infinitesimal Cherednik algebras of
 , arxiv:0810.2001 (2008).
Similar Articles:
Retrieve articles in Representation Theory
with MSC
(2010):
17-XX
Retrieve articles in all Journals with MSC
(2010):
17-XX
Additional Information:
Akaki
Tikaradze
Affiliation:
Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
Email:
atikara@utnet.utoledo.edu
DOI:
10.1090/S1088-4165-10-00363-8
PII:
S 1088-4165(10)00363-8
Received by editor(s):
May 5, 2009
Received by editor(s) in revised form:
July 7, 2009
Posted:
January 4, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
