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

References in corpus (1)

• Lattice $W$ algebras and quantum groups

Cited by in corpus (1)

• Heisenberg-Type Families in $U_q(\widehat{s{l}_2})$