New boson representations of the sl q (2) with multiplicity two and new solutions to the Yang-Baxter equation atq p =1

Whenq is a root of unity, the representations of the quantum universal enveloping algebra sl _q (2) with multiplicity two are constructed from theq-deformed boson realization with an arbitrary parameter which is in a very general form and is first presented in this Letter. The new solutions to the Yang-Baxter equation are obtained from these representations through the universalR-matrix.This work is supported in part by the National Foundation of Natural Science of China.