Highest Weight $U_q[sl(n)]$ Modules and Invariant Integrable n-State Models with Periodic Boundary Conditions"

TL;DR

This paper computes weights for Bethe vectors in an RSOS model with periodic boundary conditions, demonstrating they are highest weight vectors and deriving their q-dimensions, advancing understanding of $U_q[sl(n)]$ invariant integrable models.

Contribution

It introduces a method to compute weights of Bethe vectors in $U_q[sl(n)]$ models and establishes their highest weight property, providing explicit q-dimensions of associated irreducible representations.

Findings

Bethe vectors are highest weight vectors.

Explicit q-dimensions of irreducible representations are derived.

The model maintains $U_q[sl(n)]$ invariance with periodic boundary conditions.

Abstract

The weights are computed for the Bethe vectors of an RSOS type model with periodic boundary conditions obeying $U_q[sl(n)]$ ($q=\exp(i\pi/r)$) invariance. They are shown to be highest weight vectors. The q-dimensions of the corresponding irreducible representations are obtained.