Nonstandard coproducts and the Izergin-Korepin open spin chain

TL;DR

This paper investigates the symmetries of transfer matrices in the Izergin-Korepin open spin chain, revealing nonstandard coproduct structures for certain boundary conditions and exploring their implications.

Contribution

It demonstrates that transfer matrices associated with non-identity K matrices possess U_q(o(3)) symmetry with a nonstandard coproduct, extending understanding of boundary symmetries.

Findings

Transfer matrices with non-identity K matrices have U_q(o(3)) symmetry.

These symmetries involve a nonstandard coproduct structure.

Implications of these symmetries are briefly discussed.

Abstract

Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using these R and K matrices, one can construct transfer matrices for open integrable quantum spin chains. The transfer matrix corresponding to the identity matrix K=1 is known to have U_q(o(3)) symmetry. We argue here that the transfer matrices corresponding to the other two K matrices also have U_q(o(3)) symmetry, but with a nonstandard coproduct. We briefly explore some of the consequences of this symmetry.