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Construction of Yangian algebra through a multideformation parameter dependent rational R matrix

Sep, 1994
14 pages
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Report number:
  • IMSC-94-38,
  • IMSC-PREPRINT-94-38
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Abstract:
Yang-Baxterising a braid group representation associated with multideformed version of GLq(N)GL_{q}(N) quantum group and taking the corresponding q→1q\rightarrow 1 limit, we obtain a rational RR-matrix which depends on (1+N(N−1)2)\left ( 1+ {N(N-1) \over 2} \right ) number of deformation parameters. By using such rational RR-matrix subsequently we construct a multiparameter dependent extension of Y(glN)Y(gl_N) Yangian algebra and find that this extended algebra leads to a modification of usual asymptotic condition on monodromy matrix T(λ)T(\lambda ), at λ→∞ \lambda \rightarrow \infty limit. Moreover, it turns out that, there exists a nonlinear realisation of this extended algebra through the generators of original Y(glN)Y(gl_N) algebra. Such realisation interestingly provides a novel (1+N(N−1)2)\left ( 1 + { N(N-1) \over 2 } \right ) number of deformation parameter dependent coproduct for standard Y(glN)Y(gl_N) algebra.
Note:
  • 14 pages plain LATEX