Discrete Quantum DrinfeldSokolov Correspondence
Abstract
We construct a discrete quantum version of the DrinfeldSokolov correspondence for the sineGordon system. The classical version of this correspondence is a birational Poisson morphism between the phase space of the discrete sineGordon 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 sineGordon 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2002
 DOI:
 10.1007/s002200200626
 arXiv:
 arXiv:math/0106125
 Bibcode:
 2002CMaPh.226..627G
 Keywords:

 Mathematics  Quantum Algebra;
 35Q53;
 82B20;
 81R50
 EPrint:
 Latex2e, 33 pages