R-matrices for the adjoint representations of Uq(so(n))

TL;DR

This paper computes a two-parameter R-matrix that generalizes the trigonometric R-matrix for the minimal affinizations of the adjoint representations of classical Lie algebras so(n) and sp(n).

Contribution

It introduces a unified two-parameter R-matrix framework for the adjoint representations of classical Lie algebras, extending previous specific cases.

Findings

Derived a two-parameter R-matrix for so(n) and sp(n) adjoint representations.

Specializes to known trigonometric R-matrices for minimal affinizations.

Provides a basis for further algebraic and quantum integrable systems studies.

Abstract

We calculate a two-parameter R-matrix which specialises to the trigonometric R-matrix of the minimal affinisation of the adjoint representation of each of the classical simple Lie algebras so(n) and sp(n).