Gaussian generators for the Yangian associated with the Lie superalgebra $\mathfrak{osp}(1|2m)$

Abstract

We give a new presentation of the Yangian for the orthosymplectic Lie superalgebra $\mathfrak{osp}_{1|2m}$. It relies on the Gauss decomposition of the generator matrix in the $R$-matrix presentation. The defining relations between the Gaussian generators are derived from a new version of the Drinfeld-type presentation of the Yangian for $\mathfrak{osp}_{1|2}$ and some additional relations in the Yangian for $\mathfrak{osp}_{1|4}$ by an application of the embedding theorem for the super-Yangians.