Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials

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1. [AI] Askey, R. and Ismail, Mourad E.-H.: A generalization of ultraspherical polynomials, Studies in Pure Math. (P. Erdös, ed.), Birkhäuser, 1983, pp. 55-78. Zbl0532.33006MR820210
2. [C1] Cherednik, I.: Double affine Hecke algebras and Macdonald's conjectures, Annals of Math.141 (1995) 191-216. Zbl0822.33008MR1314036
3. [C2] Cherednik, I.: Macdonald's evaluation conjectures and difference Fourier transform, preprint, December 1994, q-alg/9412016. Zbl0854.22021
4. [CK] De Concini, C. and Kac, V.G.: Representations of quantum groups at roots of 1, Operator algebras, Unitary Representations, Enveloping Algebras and Invariant Theory (A. Connes et al, eds.), Birkhäuser, 1990, pp. 471-506. Zbl0738.17008MR1103601
5. [D] Drinfeld, V.G.: Quantum groups, Proc. Int. Congr. Math., Berkeley, 1986, pp. 798-820 Zbl0667.16003MR934283
6. [EK1] Etingof, P.I. and Kirillov, A.A., Jr.: On a unified representation-theoretic approach to the theory of special functions, Funktsion. analiz i ego prilozh. 28 (1994) no. 1, 91-94 (in Russian). Zbl0868.33010MR1275729
7. [EK2] Etingof, P.I. and Kirillov, A.A., Jr.: Macdonald's polynomials and representations of quantum groups, Math. Res. Let.1 (1994) no. 3, 279-296. Zbl0833.17007MR1302644
8. [ES] Etingof, P.I. and Styrkas, K.: Algebraic integrability of Schrödinger operators and representations of Lie algebras, preprint, hep-th/9403135 (1994), to appear in Compositio Math. Zbl0861.17003MR1353287
9. [J] Jimbo, M.A.: A q-difference analogue of Ug and the Yang-Baxter equation, Lett. Math. Phys.10 (1985) 62-69. Zbl0587.17004MR797001
10. [L] Lusztig, G.: Introduction to quantum groups, Birkhäuser, Boston, 1993. Zbl0788.17010MR1227098
11. [M1] Macdonald, I.G.: A new class of symmetric functions, Publ. I.R.M.A.Strasbourg, 372/S-20, Actes 20 Séminaire Lotharingien (1988), 131-171. Zbl0962.05507
12. [M2] Macdonald, I.G.: Orthogonal polynomials associated with root systems, preprint (1988). MR1817334
13. [RT1] Reshetikhin, N. and Turaev, V.: Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys.127 (1990) 1-26. Zbl0768.57003MR1036112
14. [RT2] Reshetikhin, N. and Turaev, V.: Invariants of 3-manifolds via link polynomials and quantum groups, Inv. Math.103 (1991) 547-597. Zbl0725.57007MR1091619
15. [T] Tanisaki, T.: Killing forms, Harish-Chandra isomorphisms and universal R-matrices for quantum algebras, Infinite Analysis, part A and part B (Kyoto, 1991), Adv. Ser. Math. Phys.17, World Scientific, pp. 941-961. Zbl0870.17007MR1187582