Quantum principal commutative subalgebra in the nilpotent part of Uqs2 and lattice KdV variables
Abstract
We propose a quantum lattice version of Feigin and E. Frenkel's constructions, identifying the KdV differential polynomials with functions on a homogeneous space under the nilpotent part of s2. We construct an action of the nilpotent part Uq n+ of Uqs2 on their lattice counterparts, and embed the lattice variables in a Uq n+-module, coinduced from a quantum version of the principal commutative subalgebra, which is defined using the identification of Uq n+ with its coordinate algebra.
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