Double affine hecke algebras, knizhnik-zamolodchikov equations, and macdonald’s operators

International Mathematics Research Notices

Volumn 1992, Issue 9, 1992, Pages 171-180

  Cherednik, Ivan ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

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[No Author keywords available]

Indexed keywords

EID: 84963009194     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/S1073792892000199     Document Type: Article

References (18)

1. K. Aomoto, “A note on holonomie q-difference systems” in Algebraic Analysis: Papers Dedicated to Professor Mikio Sato, Volume 1, ed. by M. Kashiwara and T. Kawai, Academic Press, San Diego, 1988, 25-28.
2. I. N. Bernstein, I. M. Gelfand, and S. I. Gelfand, Schubert cells and the cohomology of G/P, Russian Math. Surveys 28 (1973), 1-26.
3. N. Bourbaki, Groupes et algébres de Lie, Chapitres 4-6, Hermann, Paris, 1969.
4. I. Cherednik, Quantum Knizhnik-Zamolodchikov equations and affine root systems, preprint RIMS-862, 1992, to appear in Comm. Math. Phys.
5. I. Cherednik, Integration of quantum many-body problems by affine Knizhnik-Zamolodchikov equations, preprint RIMS-776, 1991, submitted to Adv. Math.
6. I. Cherednik, A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras, Invent. Math. 106 (1991), 411-432.
7. M. Demazure, Désingularisation des variétés de Schubert géneralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53-88.
8. I. B. Frenkel and N. Yu. Reshetikhin, Quantum affine algebras and holonomie difference equations, Comm. Math. Phys. 146 (1991), 1-60.
9. G. J. Heckman, An elementary approach to the hypergeometric shift operator of Opdam, Invent. Math. 103 (1991), 341-350.
10. D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), 153-215.
11. B. Kostant and S. Kumar, T-equivariant K-theory of generalized flag varieties, J. Differential Geom. 32(1990), 549-603.
12. H. van der Lek, “Extended Artin groups” in Singularities, Volume 1, ed. by P. Orlik, Proc. Symp. Pure Math. 40, Amer. Math. Soc., Providence, 1983, 117-122.
13. G. Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), 599-685.
14. I. G. Macdonald, “A new class of symmetric functions” in Actes Séminaire Lotharingen, Publ. Inst. Rech. Math. Adv., Strasbourg, 1988, 131-171.
15. I. G. Macdonald, “Orthogonal polynomials associated with root systems” in Orthogonal Polynomials, Proceedings, Columbus, 1989, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 294, Kluwer, Dordrecht, 1990, 311-318.
16. A. Matsuo, Knizhnik-Zamolodchikov-type equations and zonal spherical functions, preprint RIMS-750, 1991.
17. K. Saito, Extended affine root systems J, Publ. Res. Inst. Math. Sci. 21 (1985), 75-179.
18. F. A. Smirnov, A general formula for soliton form factors in the quantum sine-Gordon model, J. Phys. A 19 (1986), L575-L578.