R matrix for generalized quantum group of type A

The generalized quantum group U(ϵ) of type A is an affine analogue associated to a general linear Lie superalgebra glM|N. We prove that there exists unique R matrix on the tensor product fundamental representations for arbitrary parameter sequence ϵ corresponding non-conjugate Borel subalgebra give explicit description its spectral decomposition, and then as application, construct family finite-dimensional irreducible U(ϵ)-modules which have subspaces isomorphic Kirillov-Reshetikhin modules usual AM−1(1) or AN−1(1).