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On some representations of the rational Cherednik algebra
Author(s):
Tatyana
Chmutova;
Pavel
Etingof
Journal:
Represent. Theory
7
(2003),
641-650.
MSC (2000):
Primary 16G10;
Secondary 16Sxx, 20C08
Posted:
November 21, 2003
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Abstract:
We study lowest weight representations of the rational Cherednik algebra attached to a complex reflection group  . In particular, we generalize a number of previous results due to Berest, Etingof, and Ginzburg.
References:
-
- [BEG]
- Yu. Berest, P. Etingof, V. Ginzburg, Finite dimensional representations of rational Cherednik algebras, Int. Math. Res. Not. 2003, no. 19, 1053-1088.
- [BEG1]
- Yuri Berest, Pavel Etingof, Victor Ginzburg, Cherednik algebras and differential operators on quasi-invariants, Duke Math. J. 118, no. 2 (2003), 279-337.
- [E]
- Eisenbud, David, Commutative algebra with a view toward algebraic geometry. Graduate Texts in Mathematics, 150, Springer-Verlag, New York, 1995. MR 97a:13001
- [EG]
- P. Etingof, V. Ginzburg, Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2002), 243-348. MR 2003b:16021
- [Du]
- C. Dunkl, Intertwining operators and polynomials associated with the symmetric group, Monatshefte Math. 126 (1998), 181-209. MR 2001b:33021
- [DO]
- C. F. Dunkl, E. M. Opdam, Dunkl operators for complex reflection groups, Proc. London Math. Soc. (3) 86 (2003), no. 1, 70-108.
- [Go]
- Iain Gordon, On the quotient ring by diagonal harmonics, math.RT/0208126.
- [GGOR]
- Victor Ginzburg, Nicolas Guay, Eric Opdam, Raphael Rouquier, On the category O for rational Cherednik algebras, math.RT/0212036.
- [S]
- Serre, J.-P., Algebrè locale. Multiplicités, Lect. Notes in Math., 11, Springer-Verlag, Berlin, New York, 1965. MR 34:1352
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Additional Information:
Tatyana
Chmutova
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email:
chmutova@math.harvard.edu
Pavel
Etingof
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
etingof@math.mit.edu
DOI:
10.1090/S1088-4165-03-00214-0
PII:
S 1088-4165(03)00214-0
Received by editor(s):
April 8, 2003
Received by editor(s) in revised form:
October 10, 2003
Posted:
November 21, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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