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

B. Basu-Mallick·P. Ramadevi
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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 $T(λ)$, at $ λ\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.

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B. Basu-Mallick, P. Ramadevi. 1994-09-28. Construction of Yangian algebra through a multi-deformation parameter dependent rational $R$-matrix. https://arxiv.org/abs/hep-th/9409178

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