Colored extension of GL q(2) and its dual algebra

We address the problem of duality between the colored extension of the quantized algebra of functions on a group and that of its quantized universal enveloping algebra, i.e., its dual. In particular, we derive explicitly the algebra dual to the colored extension of GL _q(2) using the colored RLL relations and exhibit its Hopf structure. This leads to a colored generalization of the R-matrix procedure to construct a bicovariant differential calculus on the colored version of GL _q(2). In addition, we also propose a colored generalization of the geometric approach to quantum group duality given by Sudbery and Dobrev.