JILIN UNIV,DEPT PHYS,CHANGCHUN 130021,PEOPLES R CHINA
; INST HIGH ENERGY PHYS,BEIJING 100039,PEOPLES R CHINA
In this letter, a new class of representations of the braid groups B-N,I-i-1+T+I-N-i-1 is constructed. It is proved that those representations contain three kinds of irreducible representations: the trivial (identity) one, the Burau one, and anew N-dimensional one. The explicit form of the N-dimensional irreducible representation of the braid group BN is given.