Quantum symmetric spaces

J. Donin; S. Shnider

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arXiv · hep-th/9412031

Quantum symmetric spaces

J. Donin·S. Shnider

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Abstract

Let $G$ be a semisimple Lie group, ${\frak g}$ 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 $U_h{\frak g}$ and is commutative with respect to an involutive operator $\tilde{S}: A\otimes A \to A\otimes A$. Such a multiplication is unique. Let $M$ be a kählerian symmetric space with the canonical Poisson structure. Then we construct a $U_h{\frak g}$-invariant multiplication in $A$ which depends on two parameters and is a quantization of that structure.

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J. Donin, S. Shnider. 1994-12-04. Quantum symmetric spaces. https://arxiv.org/abs/hep-th/9412031

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