The generalized quantum group $$extract_itex$$U(e)$$/extract_itex$$ of type A is an affine analogue of quantum group associated to a general linear super algebra $$extract_itex$$gl_{M|N}$$/extract_itex$$ with respect to its arbitrary Borel subalgebra.  It is related to solutions of 3 dimensional Yang-Baxter equation.

We prove the uniqueness of $$extract_itex$$R$$/extract_itex$$ matrix on a tensor product of fundamental type representations of $$extract_itex$$U(e)$$/extract_itex$$.

Then we give an explicit description of the spectral decomposition of the $$extract_itex$$R$$/extract_itex$$ matrix and construct KR type modules of $$extract_itex$$U(e)$$/extract_itex$$.