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Contraction of the Gr,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups

Deepak Parashar, Roger J. McDermott

math.QAarXiv:math/9911194

Abstract

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

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