A Classically Singular Representation of $ su_q(n) $

TL;DR

This paper investigates a new infinite-dimensional, non-unitary representation of the quantum algebra su_q(n) that diverges in the classical limit, providing a novel solution to the Yang-Baxter equation with continuous spectral parameters.

Contribution

It introduces a classically singular, infinite-dimensional representation of su_q(n) with continuous parameters, offering a new approach to solutions of the Yang-Baxter equation.

Findings

Provides a new infinite-dimensional, non-unitary representation of su_q(n).

Demonstrates that continuous variables can serve as spectral parameters.

Offers a novel solution to the Yang-Baxter equation.

Abstract

A \rep of \sun, which diverges in the limit of \cl, is investigated. This is an infinite dimensional and a non-unitary \rep, defined for the real value of $ q, \ 0 < q < 1. $ Each \irrep is specified by $ n $ continuous variables and one discrete variable. This \rep gives a new solution of the Yang-Baxter equation, when the R-matrix is evaluated. It is shown that a continuous variables can be regarded as a spectral parameter.