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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
Published electronically: November 21, 2003
MathSciNet review: 2017070
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Abstract: We study lowest weight representations of the rational Cherednik algebra attached to a complex reflection group $W$. In particular, we generalize a number of previous results due to Berest, Etingof, and Ginzburg.

References [Enhancements On Off] (What's this?)

  • [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

Pavel Etingof
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

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

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