On some representations of the rational Cherednik algebra
Authors:
Tatyana Chmutova and Pavel Etingof
Journal:
Represent. Theory 7 (2003), 641650
MSC (2000):
Primary 16G10; Secondary 16Sxx, 20C08
Published electronically:
November 21, 2003
MathSciNet review:
2017070
Fulltext PDF Free Access
Abstract 
References 
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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, 10531088.
 [BEG1]
Yuri Berest, Pavel Etingof, Victor Ginzburg, Cherednik algebras and differential operators on quasiinvariants, Duke Math. J. 118, no. 2 (2003), 279337.
 [E]
David
Eisenbud, Commutative algebra, Graduate Texts in Mathematics,
vol. 150, SpringerVerlag, New York, 1995. With a view toward
algebraic geometry. MR 1322960
(97a:13001)
 [EG]
Pavel
Etingof and Victor
Ginzburg, Symplectic reflection algebras, CalogeroMoser space, and
deformed HarishChandra homomorphism, Invent. Math.
147 (2002), no. 2, 243–348. MR 1881922
(2003b:16021), http://dx.doi.org/10.1007/s002220100171
 [Du]
Charles
F. Dunkl, Intertwining operators and polynomials associated with
the symmetric group, Monatsh. Math. 126 (1998),
no. 3, 181–209. MR 1651774
(2001b:33021), http://dx.doi.org/10.1007/BF01367762
 [DO]
C. F. Dunkl, E. M. Opdam, Dunkl operators for complex reflection groups, Proc. London Math. Soc. (3) 86 (2003), no. 1, 70108.
 [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]
JeanPierre
Serre, Algèbre locale. Multiplicités, Cours au
Collège de France, 1957–1958, rédigé par Pierre
Gabriel. Seconde édition, 1965. Lecture Notes in Mathematics,
vol. 11, SpringerVerlag, BerlinNew York, 1965 (French). MR 0201468
(34 #1352)
 [BEG]
 Yu. Berest, P. Etingof, V. Ginzburg, Finite dimensional representations of rational Cherednik algebras, Int. Math. Res. Not. 2003, no. 19, 10531088.
 [BEG1]
 Yuri Berest, Pavel Etingof, Victor Ginzburg, Cherednik algebras and differential operators on quasiinvariants, Duke Math. J. 118, no. 2 (2003), 279337.
 [E]
 Eisenbud, David, Commutative algebra with a view toward algebraic geometry. Graduate Texts in Mathematics, 150, SpringerVerlag, New York, 1995. MR 97a:13001
 [EG]
 P. Etingof, V. Ginzburg, Symplectic reflection algebras, CalogeroMoser space, and deformed HarishChandra homomorphism, Invent. Math. 147 (2002), 243348. MR 2003b:16021
 [Du]
 C. Dunkl, Intertwining operators and polynomials associated with the symmetric group, Monatshefte Math. 126 (1998), 181209. 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, 70108.
 [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, SpringerVerlag, 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:
http://dx.doi.org/10.1090/S1088416503002140
PII:
S 10884165(03)002140
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
