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5 papers · 1 filter
Duality for Coloured Quantum Groups
Deepak Parashar
Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L^{\pm} functionals are constructed and the dual alg…
On some two parameter Quantum and Jordanian deformations, and their Coloured extensions
Deepak Parashar, Roger J. McDermott
This paper suveys some recent algebraic developments in two parameter Quantum deformations and their Nonstandard (or Jordanian) counterparts. In particular, we discuss the contract…
Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups
Deepak Parashar, Roger J. McDermott
The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contractio…
Inhomogeneous Multiparameter Jordanian Quantum Groups by Contraction
Roger J. McDermott, Deepak Parashar
It is known that the inhomogeneous quantum group IGL_{q,r}(2) can be constructed as a quotient of the multiparameter q-deformation of GL(3). We show that a similar result holds for…
Realisations of Quantum GL_p,q(2) and Jordanian GL_h,h'(2)
Deepak Parashar, Roger J. McDermott
The quantum group GL_p,q(2) is known to be related to the Jordanian GL_h,h'(2) via a contraction procedure. It can also be realised using the generators of the Hopf algebra G_r,s.…