Trigonometric solutions of triangle equations. Simple lie superalgebras

Abstract

Trigonometric solutions of the graded triangle equation are constructed for the fundamental representations of all simple (nonexceptional) Lie superalgebras with nondegenerate metric. In Sec. 1, we introduce the concept of Z/sub 2/ graded spaces and give the basic definitions. In Sec. 2, we determine fundamental representations of the Lie superalgebras sl(m/vert bar/n) and osp(2r/vert bar/s) and give explicit realizations of the Coxeter automorphisms. In secs. 3 and 4, we give the trigonometric solutions of the graded triangle equation (quantum R matrices).