Singular polynomials for the symmetric groups

International Mathematics Research Notices

Volumn , Issue 67, 2004, Pages 3607-3635

  Dunkl, Charles F ^a  

^a University of Virginia   (United States)

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[No Author keywords available]

Indexed keywords

EID: 25644453453     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792804140610     Document Type: Article

References (15)

1. Y. Berest, P. Etingof, and V. Ginzburg, Cherednik algebras and differential operators on quasiinvariants, Duke Math. J. 118 (2003), no. 2, 279-337.
2. _, Finite-dimensional representations of rational Cherednik algebras, Int. Math. Res. Not. 2003 (2003), no. 19, 1053-1088.
3. T. Chmutova and P. Etingof, On some representations of the rational Cherednik algebra, Represent. Theory 7 (2003), 641-650.
4. C. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989), no. 1, 167-183.
5. _, Intertwining operators and polynomials associated with the symmetric group, Monatsh. Math. 126 (1998), no. 3, 181-209.
6. _, Singular polynomials for the symmetric group and Krawtchouk polynomials, preprint, 2003, http://www.arxiv.org/abs/math.QA/0310249.
7. C. Dunkl, M. de Jeu, and E. Opdam, Singular polynomials for finite reflection groups, Trans. Amer. Math. Soc. 346 (1994), no. 1, 237-256.
8. C. Dunkl and Y. Xu, Orthogonal Polynomials of Several Variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001.
9. P. Etingof and V. Ginzburg, Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2002), no. 2, 243-348.
10. V. Ginzburg, N. Guay, E. Opdam, and R. Rouquier, On the category Ο for rational Cherednik algebras, Invent. Math. 154 (2003), no. 3, 617-651.
11. F. Knop and S. Sahi, A recursion and a combinatorial formula for Jack polynomials, Invent. Math. 128 (1997), no. 1, 9-22.
12. I. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995.
13. G. Murphy, A new construction of Young's seminormal representation of the symmetric groups, J. Algebra 69 (1981), no. 2, 287-297.
14. E. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), no. 1, 75-121.
15. R. Stanley, Enumerative Combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999.