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Quantum group structure and local fields in the algebraic approach to 2D gravity
Teoretičeskaâ i matematičeskaâ fizika, Tome 104 (1995) no. 1, pp. 158-191 Cet article a éte moissonné depuis la source Math-Net.Ru

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This review contains a summary of work by J. L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev. 
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J. Schnittger. Quantum group structure and local fields in the algebraic approach to 2D gravity. Teoretičeskaâ i matematičeskaâ fizika, Tome 104 (1995) no. 1, pp. 158-191. http://geodesic.mathdoc.fr/item/TMF_1995_104_1_a11/

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