Geodesic
On Cherednik-Macdonald-Mehta identities
Etingof, Pavel1 ; Kirillov, Alexander, Jr.2
1 Department of Mathematics, Harvard University, Cambridge, MA 02138
2 Department of Mathematics, MIT, Cambridge, MA 02139
Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 43-47

Voir la notice de l'article provenant de la source American Mathematical Society

In this note we give a proof of Cherednik’s generalization of Macdonald–Mehta identities for the root system $A_{n-1}$, using representation theory of quantum groups. These identities give an explicit formula for the integral of a product of Macdonald polynomials with respect to a “difference analogue of the Gaussian measure”. They were suggested by Cherednik, who also gave a proof based on representation theory of affine Hecke algberas; our proof gives a nice interpretation for these identities in terms of representations of quantum groups and seems to be simpler than that of Cherednik.
DOI : 10.1090/S1079-6762-98-00045-6

Etingof, Pavel 1 ; Kirillov, Alexander, Jr. 2

1 Department of Mathematics, Harvard University, Cambridge, MA 02138
2 Department of Mathematics, MIT, Cambridge, MA 02139 
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Etingof, Pavel; Kirillov, Alexander, Jr. On Cherednik-Macdonald-Mehta identities. Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 43-47. doi: 10.1090/S1079-6762-98-00045-6

[1] Cherednik, Ivan Double affine Hecke algebras and Macdonald’s conjectures Ann. of Math. (2) 1995 191 216

[2] Etingof, Pavel I., Kirillov, Alexander A., Jr. Macdonald’s polynomials and representations of quantum groups Math. Res. Lett. 1994 279 296

[3] Etingof, Pavel I., Kirillov, Alexander A., Jr. Representation-theoretic proof of the inner product and symmetry identities for Macdonald’s polynomials Compositio Math. 1996 179 202

[4] Kassel, Christian Quantum groups 1995

[5] Kirillov, Alexander A., Jr. On an inner product in modular tensor categories J. Amer. Math. Soc. 1996 1135 1169

[6] Kostant, Bertram On Macdonald’s 𝜂-function formula, the Laplacian and generalized exponents Advances in Math. 1976 179 212

[7] Macdonald, I. G. Symmetric functions and Hall polynomials 1995

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