Quantum symmetric spaces

J. Donin, S. Shnider

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld-Jimbo quantum group Uhg and is commutative with respect to an involutive operator S ̃: A ⊗ A → A ⊗ A. Such a multiplication is unique. Let M be a kählerian symmetric space with the canonical Poisson structure. Then we construct a Uhg-invariant multiplication in A which depends on two parameters and is a quantization of that structure.

Original languageEnglish
Pages (from-to)103-115
Number of pages13
JournalJournal of Pure and Applied Algebra
Issue number1-3
StatePublished - 12 May 1995


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