DUALITY FOR MULTIPARAMETER QUANTUM DEFORMATION OF THE SUPERGROUP GL(MN)/

We find the Hopf superalgebra U-uq, which is in duality with the multi parameter quantum deformation GL(uq)(m/n) of the supergroup GL(m/n). N aturally U-uq is a multiparameter deformation of the superalgebra U(gl (m/n)). We show that as a commutation algebra we have the classical st ructure, namely a split into two subalgebras: U-uq congruent to U' x K , where U' is isomorphic to the standard one-parameter deformation U-u (sl(m/n)), and K is central in U-uq for m not equal n. However, as a c oalgebra U-uq cannot be split in this way, as only K is a Hopf subalge bra, while U' is not a Hopf subalgebra unless m = n = 1 or some specia l relations between the parameters exist. These special relations are established and used to obtain explicit multiparameter Hopf superalgeb ra deformations of U(sl(m/n)).