The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair

Welleda Baldoni; Pierluigi Möseneder Frajria

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 4, page 1179-1214
  • ISSN: 0373-0956

Abstract

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Let G / K a noncompact symmetric space with Iwasawa decomposition K A N . The Harish-Chandra homomorphism is an explicit homomorphism between the algebra of invariant differential operators on G / K and the algebra of polynomials on A that are invariant under the Weyl group action of the pair ( G , A ) . The main result of this paper is a generalization to the quantum setting of the Harish-Chandra homomorphism in the case of G / K being an hermitian (classical) symmetric space

How to cite

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Baldoni, Welleda, and Frajria, Pierluigi Möseneder. "The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair." Annales de l'institut Fourier 49.4 (1999): 1179-1214. <http://eudml.org/doc/75377>.

@article{Baldoni1999,
abstract = {Let $G/K$ a noncompact symmetric space with Iwasawa decomposition $KAN$. The Harish-Chandra homomorphism is an explicit homomorphism between the algebra of invariant differential operators on $G/K$ and the algebra of polynomials on $A$ that are invariant under the Weyl group action of the pair $(G,A)$. The main result of this paper is a generalization to the quantum setting of the Harish-Chandra homomorphism in the case of $G/K$ being an hermitian (classical) symmetric space},
author = {Baldoni, Welleda, Frajria, Pierluigi Möseneder},
journal = {Annales de l'institut Fourier},
keywords = {hermitian symmetric space; quantum group; Harish-Chandra homomorphism; algebra of differential operators; quantized enveloping algebra},
language = {eng},
number = {4},
pages = {1179-1214},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair},
url = {http://eudml.org/doc/75377},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Baldoni, Welleda
AU - Frajria, Pierluigi Möseneder
TI - The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 4
SP - 1179
EP - 1214
AB - Let $G/K$ a noncompact symmetric space with Iwasawa decomposition $KAN$. The Harish-Chandra homomorphism is an explicit homomorphism between the algebra of invariant differential operators on $G/K$ and the algebra of polynomials on $A$ that are invariant under the Weyl group action of the pair $(G,A)$. The main result of this paper is a generalization to the quantum setting of the Harish-Chandra homomorphism in the case of $G/K$ being an hermitian (classical) symmetric space
LA - eng
KW - hermitian symmetric space; quantum group; Harish-Chandra homomorphism; algebra of differential operators; quantized enveloping algebra
UR - http://eudml.org/doc/75377
ER -

References

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  10. [10] B. KOSTANT and S. SAHI, The Capelli identity, tube domains and the generalized Laplace transform, Adv. in Math., 87 (1991), 71-92. Zbl0748.22008MR92h:22033
  11. [11] G. LUSZTIG, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math., 70 (1988), 237-249. Zbl0651.17007MR89k:17029
  12. [12] G. LUSZTIG, Quantum groups at root of 1, Geom. Dedicata, 35 (1990), 89-114. Zbl0714.17013MR91j:17018
  13. [13] N. YU. RESHETIKHIN, L.A. TAKHTADZHYAN, and L.D. FADDEEV, Quantization of Lie groups and Lie algebras, Leningrad Math. J., 1 (1990), 193-225. Zbl0715.17015MR90j:17039
  14. [14] N. R. WALLACH, The analytic continuation of the discrete series II, Trans. Amer. Math. Soc., 251 (1979), 19-37. Zbl0419.22018MR81a:22009

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