Quantum symmetric spaces

Details Quantum symmetric spaces Quantum symmetric spaces

1994-12-04

arxiv.org/abs/hep-th/9412031v1

J. Pure Appl. Algebra 100 (1995) 103

Physics

High Energy Physics

High Energy Physics - Theory

16 pp, LaTeX

Scientific paper

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 k\"{a}hlerian 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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