Quantum principal commutative subalgebra in the nilpotent part of $U_q\widehat{s\ell}_2$ and lattice KdV variables

Details Quantum principal commutative subalgebra in the nilpotent part of $U_q\widehat{s\ell}_2$ and lattice KdV variables Quantum principal commutative subalgebra in the nilpotent part of $U_q\widehat{s\ell}_2$ and lattice KdV variables

1994-02-25

arxiv.org/abs/hep-th/9402145v1

Commun.Math.Phys. 170 (1995) 197-206

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/BF02099445

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 $\widehat{s\ell}_2$. We construct an action of the nilpotent part $U_q\widehat n_+$ of $U_q\widehat{s\ell}_2$ on their lattice counterparts, and embed the lattice variables in a $U_q\widehat n_+$-module, coinduced from a quantum version of the principal commutative subalgebra, which is defined using the identification of $U_q\widehat n_+$ with its coordinate algebra.

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