arXiv:q-alg/9511028v2 26 Feb 1997 q-alg/9511028 TIFR/TH/95-54 IMSc/95/29 November 1995 MULTIPARAMETRIC AND COLOURED EXTENSIONS OF THE QUANTUM GROUP GL q (N ) AND THE YANGIAN ALGEBRA Y (gl N ) THROUGH A SYMMETRY TRANSFORMATION OF THE YANG-BAXTER EQUATION B. BASU-MALLICK ∗ Theoretical Physics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400 005, India P. RAMADEVI † , R. JAGANNATHAN ‡ The Institute of Mathematical Sciences, C.I.T.Campus, Tharamani, Madras-600 113, India Inspired by Reshetikhin’s twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general ‘symmetry transformation’ of the ‘particle conserving’ R-matrix is found such that the resulting multiparametric R-matrix, with a spectral parameter as well as a colour parameter, is also a solution of the Yang-Baxter equation (YBE). The corresponding transformation of the quantum YBE reveals a new relation between the associated quantized algebra and its multiparametric deformation. As applications of this general relation to some particular cases, multiparametric and coloured extensions of the quantum group GL q (N ) and the Yangian algebra Y (gl N ) are investigated and their explicit realizations are also discussed. Possible interesting physical applications of such extended Yangian algebras are indicated. To appear in Int. J. Mod. Phys. A * E-mail : biru@theory.tifr.res.in † E-mail : rama@imsc.ernet.in ‡ E-mail : jagan@imsc.ernet.in