A polynomial formula for the solution of 3D reflection equation

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.

14 pages. A minor correction in C_{ij} in section 2.1

References in corpus (2)

• Quantum geometry of 3-dimensional lattices
• Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_q(D_{n+1}^{(2)}),U_q(A_{2n}^{(2)})$ and $U_q(C_n^{(1)})$

Cited by in corpus (1)

• Combinatorial Yang-Baxter maps arising from tetrahedron equation