Contraction of the Gr,s quantum group to its nonstandard analog and corresponding colored quantum groups

Abstract

The quantum group Gr,s provides a realization of the two parameter quantum GLp,q(2), which is known to be related to the two parameter nonstandard GLh,h′(2) group via the contraction method. We apply the contraction procedure to Gr,s and obtain a new Jordanian quantum group Gm,k. Furthermore, we provide a realization of GLh,h′(2) in terms of Gm,k. The contraction procedure is then extended to the colored quantum group GLrλ,μ(2) to yield a new Jordanian quantum group GLmλ,μ(2). Both Gr,s and Gm,k are then generalized to their colored versions, which in turn provide similar realizations of GLrλ,μ(2) and GLmλ,μ(2).