Steklov Institute of Mathematics at St.Petersburg

PREPRINT 22/2005

LATTICE MODELS WITH NONCOMPACT QUANTUM GROUP SYMMETRY

This preprint was accepted December 23, 2005

ABSTRACT:

We define and study certain integrable lattice models with 
non-compact quantum group symmetry. Their universal R-matrices 
are constructed in terms of non--compact quantum dilogarithm 
function. One of these models is a version of the XXZ quantum 
spin chain, the other turns out to be a natural lattice 
discretization of the sinh-Gordon model. Our choice of the 
quantum group representations naturally ensures self-adjointness 
of the Hamiltonian and of the integrals of motion.