On some representations of the rational Cherednik algebra

Authors:
Tatyana Chmutova and Pavel Etingof

Journal:
Represent. Theory **7** (2003), 641-650

MSC (2000):
Primary 16G10; Secondary 16Sxx, 20C08

DOI:
https://doi.org/10.1090/S1088-4165-03-00214-0

Published electronically:
November 21, 2003

MathSciNet review:
2017070

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Abstract | References | Similar Articles | Additional Information

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.

**[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:
https://doi.org/10.1090/S1088-4165-03-00214-0

Received by editor(s):
April 8, 2003

Received by editor(s) in revised form:
October 10, 2003

Published electronically:
November 21, 2003

Article copyright:
© Copyright 2003
American Mathematical Society