# 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

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topEtingof, 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. <http://eudml.org/doc/90452>.

@article{Etingof1996,

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 = {http://eudml.org/doc/90452},

volume = {102},

year = {1996},

}

TY - JOUR

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 - http://eudml.org/doc/90452

ER -

## References

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- [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
- [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
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- [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
- [M2] Macdonald, I.G.: Orthogonal polynomials associated with root systems, preprint (1988). MR1817334
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- [RT2] Reshetikhin, N. and Turaev, V.: Invariants of 3-manifolds via link polynomials and quantum groups, Inv. Math.103 (1991) 547-597. Zbl0725.57007MR1091619
- [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

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