Structure and representations on the quantum supergroup OSPq(2|2n)

Abstract

The structure and representations of the quantum supergroup OSPq(2|2n) are studied systematically. The algebra of functions on the quantum supergroup, which specifies the quantum supergroup itself, is taken to be the superalgebra generated by the matrix elements of the vector representation of the quantized universal superalgebra Uq(osp(2|2n)). It is shown that the algebra of functions is dense in the full dual Uq(osp(2|2n))* of Uq(osp(2|2n)) and possesses a Hopf superalgebra structure. The left integral and right integral on the quantum supergroup are discussed. Induced representations are developed using the noncommutative geometry of quantum homogeneous supervector bundles, and a geometric realization of irreducible representations is obtained.