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

Pavel I. Etingof; Alexander A. Kirillov, Jr.

Compositio Mathematica (1996)

  • Volume: 102, Issue: 2, page 179-202
  • ISSN: 0010-437X

How to cite


Etingof, Pavel I., and Kirillov, Jr., Alexander A.. "Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials." Compositio Mathematica 102.2 (1996): 179-202. <>.

author = {Etingof, Pavel I., Kirillov, Jr., Alexander A.},
journal = {Compositio Mathematica},
keywords = {quantum groups; Macdonald's polynomials; symmetry identities},
language = {eng},
number = {2},
pages = {179-202},
publisher = {Kluwer Academic Publishers},
title = {Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials},
url = {},
volume = {102},
year = {1996},

AU - Etingof, Pavel I.
AU - Kirillov, Jr., Alexander A.
TI - Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 102
IS - 2
SP - 179
EP - 202
LA - eng
KW - quantum groups; Macdonald's polynomials; symmetry identities
UR -
ER -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.