The Harish-Chandra homomorphism for a quantized classical Hermitian symmetric pair (Q1294737)
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scientific article; zbMATH DE number 1323233
| Language | Label | Description | Also known as |
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| English | The Harish-Chandra homomorphism for a quantized classical Hermitian symmetric pair |
scientific article; zbMATH DE number 1323233 |
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The Harish-Chandra homomorphism for a quantized classical Hermitian symmetric pair (English)
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10 August 1999
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Let \(G/K\) be an irreducible Hermitian symmetric space of the non-compact type. A quantum version \(D_q(G/K)\) of the algebra of invariant differential operators on \(G/K\) is constructed. The main result of the paper is the quantum version of the Harish-Chandra isomorphism between \(D_q(G/K)\) and the algebra of Laurent polynomials that are invariant for a certain Weyl group. This is proved for the classical cases \(A_n\), \(B_n\), \(C_n\) and \(D_n\).
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hermitian symmetric space
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quantum group
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Harish-Chandra homomorphism
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algebra of differential operators
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quantized enveloping algebra
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