CHINESE ACAD SCI,GRAD SCH,BEIJING 100039,PEOPLES R CHINA
; INST HIGH ENERGY PHYS,BEIJING 100039,PEOPLES R CHINA
; CCAST WORLD LAB,BEIJING,PEOPLES R CHINA
In this paper, both trigonometric and rational solutions to the Yang-Baxter equation associated with the spinor representations of the quantum B1 universal enveloping algebras are obtained. The corresponding representations of the braid group and the link polynomials are also computed through a standard method. The quantum Clebsch-Gordan matrix, the quantum projectors and the solutions associated with the spinor representation of the quantum B3 are presented explicitly.