no. 4
The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair
Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1179-1214.

Soit G/K un espace symétrique non compact avec décomposition d’Iwasawa KAN. L’homomorphisme d’Harish-Chandra est un homomorphisme explicite entre l’algèbre des opérateurs différentiels sur G/K et l’algèbre des polynômes sur A invariante par rapport à l’action du groupe de Weyl de la paire (G,A). Le résultat principal de cet article est une généralisation dans le cas quantique de l’homomorphisme d’Harish-Chandra pour G/K symétrique hermitien (classique).

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

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     author = {Baldoni, Welleda and Frajria, Pierluigi M\"oseneder},
     title = {The {Harish-Chandra} homomorphism for a quantized classical hermitian symmetric pair},
     journal = {Annales de l'Institut Fourier},
     pages = {1179--1214},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {4},
     year = {1999},
     doi = {10.5802/aif.1713},
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Baldoni, Welleda; Frajria, Pierluigi Möseneder. The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair. Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1179-1214. doi : 10.5802/aif.1713. https://aif.centre-mersenne.org/articles/10.5802/aif.1713/

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