FINITE DIMENSIONAL IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERGROUP UQ(GL(M/N))

Finite dimensional irreducible representations of the quantum supergroup U(q)(gl(m/n)) at both generic q and q being a root of unity are investigated systematically within the framework of the induced module construction. The representation theory is rather similar to that of gl(m/n) at generic q, but drastically different when q is a root of unity. In the latter case, atypicality conditions of highest weight irreducible representations (irreps) are substantially altered, and such finite-dimensional irreps arise that do not have highest weight and/or lowest weight vectors. As concrete examples, the irreps of U(q)(gl(2/1)) are classified.