$\ell$-weights and factorization of transfer operators

TL;DR

This paper studies the structure of $ ext{ extlbrackdbl} ext{ extlbrackdbl} ext{ extlbrackdbl}$-weights in certain quantum loop algebra representations and establishes factorization relations for transfer operators in related integrable models.

Contribution

It provides a detailed analysis of $ ext{ extlbrackdbl} ext{ extlbrackdbl}$-weights and proves new factorization formulas for transfer operators in quantum integrable systems.

Findings

Analysis of $ ext{ extlbrackdbl} ext{ extlbrackdbl}$-weights for specific representations

Proof of factorization relations for transfer operators

Application to quantum integrable systems

Abstract

We analyze the $\ell$--weights of the evaluation and $q$-oscillator representations of the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ for $l = 1$ and $l = 2$ and prove the factorization relations for the transfer operators of the associated quantum integrable systems.