Discrete quantum Drinfeld-Sokolov correspondence

Details Discrete quantum Drinfeld-Sokolov correspondence Discrete quantum Drinfeld-Sokolov correspondence

2001-06-14

arxiv.org/abs/math/0106125v1

Commun.Math.Phys. 226 (2002) 627-662

Mathematics

Quantum Algebra

Latex2e, 33 pages

Scientific paper

10.1007/s002200200626

We construct a discrete quantum version of the Drinfeld-Sokolov correspondence for the sine-Gordon system. The classical version of this correspondence is a birational Poisson morphism between the phase space of the discrete sine-Gordon system and a Poisson homogeneous space. Under this correspondence, the commuting higher mKdV vector fields correspond to the action of an Abelian Lie algebra. We quantize this picture (1) by quantizing this Poisson homogeneous space, together with the action of the Abelian Lie algebra, (2) by quantizing the sine-Gordon phase space, (3) by computing the quantum analogues of the integrals of motion generating the mKdV vector fields, and (4) by constructing an algebra morphism taking one commuting family of derivations to the other one.

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