On some representations of the rational Cherednik algebra
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- by Tatyana Chmutova and Pavel Etingof PDF
- Represent. Theory 7 (2003), 641-650 Request permission
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.
[BEG]BEG Yu. Berest, P. Etingof, V. Ginzburg, Finite dimensional representations of rational Cherednik algebras, Int. Math. Res. Not. 2003, no. 19, 1053–1088.
[BEG1]BEG1 Yuri Berest, Pavel Etingof, Victor Ginzburg, Cherednik algebras and differential operators on quasi-invariants, Duke Math. J. 118, no. 2 (2003), 279–337.
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- Pavel Etingof and Victor Ginzburg, Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2002), no. 2, 243–348. MR 1881922, DOI 10.1007/s002220100171
- Charles F. Dunkl, Intertwining operators and polynomials associated with the symmetric group, Monatsh. Math. 126 (1998), no. 3, 181–209. MR 1651774, DOI 10.1007/BF01367762 [DO]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]Go Iain Gordon, On the quotient ring by diagonal harmonics, math.RT/0208126. [GGOR]GGOR Victor Ginzburg, Nicolas Guay, Eric Opdam, Raphael Rouquier, On the category O for rational Cherednik algebras, math.RT/0212036.
- Jean-Pierre Serre, Algèbre locale. Multiplicités, Lecture Notes in Mathematics, vol. 11, Springer-Verlag, Berlin-New York, 1965 (French). Cours au Collège de France, 1957–1958, rédigé par Pierre Gabriel; Seconde édition, 1965. MR 0201468, DOI 10.1007/978-3-662-21576-0
- Tatyana Chmutova
- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
- Email: email@example.com
- Pavel Etingof
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 289118
- Email: firstname.lastname@example.org
- Received by editor(s): April 8, 2003
- Received by editor(s) in revised form: October 10, 2003
- Published electronically: November 21, 2003
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2017070