QUANTUM SUPERGROUPS, LINK POLYNOMIALS AND REPRESENTATION OF THE BRAIDGENERATOR

Unlike the quantum group case, it is shown that the braid generator si gma is not always diagonalizable on V X V, V an irreducible module for a quantum supergroup. Nevertheless a generalization of the Reshetikhi n form of the braid generator, obtained previously for quantum groups, is determined corresponding to every finite dimensional standard cycl ic module V of a quantum supergroup. This result is applied to obtain a general closed formula for link polynomials arising from standard cy clic modules of a quantum supergroup belonging to a certain class. As explicit examples we determine link polynomials corresponding to the r ank 2 symmetric tensor representation of U(q)gl(m\m)! and the definin g representation of U(q)osp(2n\2n)!.