Construction of Yangian algebra through a multi-deformation parameter dependent rational $R$-matrix

Abstract

Yang-Baxterising a braid group representation associated with multideformed version of $G{L}_q(N)$ quantum group and taking the corresponding $q\to 1$ limit, we obtain a rational $R$-matrix which depends on $\left(1+\frac{N(N-1)}{2}\right)$ number of deformation parameters. By using such rational $R$-matrix subsequently we construct a multiparameter dependent extension of $Y(g{l}_N)$ Yangian algebra and find that this extended algebra leads to a modification of usual asymptotic condition on monodromy matrix $T(\lambda )$, at $\lambda \to \infty$ limit. Moreover, it turns out that, there exists a nonlinear realisation of this extended algebra through the generators of original $Y(g{l}_N)$ algebra. Such realisation interestingly provides a novel $\left(1+\frac{N(N-1)}{2}\right)$ number of deformation parameter dependent coproduct for standard $Y(g{l}_N)$ algebra.

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