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

TL;DR

This paper constructs a multi-parameter deformed Yangian algebra using a rational R-matrix derived from a multideformed quantum group, revealing new algebraic structures and coproducts.

Contribution

It introduces a novel multi-parameter extension of the Yangian algebra with a modified asymptotic condition and a nonlinear realization involving deformation parameters.

Findings

Constructed a multiparameter dependent Yangian algebra.

Discovered a nonlinear realization of the extended algebra.

Provided a deformation-dependent coproduct for Y(gl_N).

Abstract

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