A polynomial formula for the solution of 3D reflection equation

TL;DR

This paper introduces a new polynomial-based formula for solving the 3D reflection equation, linking algebraic structures with solutions in quantum integrable systems.

Contribution

It presents a novel polynomial formula associated with the quantized algebra of functions $A_q(C_2)$ for solving the 3D reflection equation.

Findings

New polynomial family in $q^2$ and four variables introduced

Explicit formula for the 3D reflection equation solution provided

Connection established between polynomials and $q$-oscillator eigenvalues

Abstract

We introduce a family of polynomials in $q^2$ and four variables associated with the quantized algebra of functions $A_q(C_2)$. A new formula is presented for the recent solution of the 3D reflection equation in terms of these polynomials specialized to the eigenvalues of the $q$-oscillator operators.