Equivalences between three presentations of orthogonal and symplectic Yangians

Abstract

We prove the equivalence of two presentations of the Yangian $Y(\mathfrak{g})$ of a simple Lie algebra $\mathfrak{g}$ and we also show the equivalence with a third presentation when $\mathfrak{g}$ is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians.

31 pages

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Cited by in corpus (24)

• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: type C
• Shifted quantum affine algebras: integral forms in type $A$ (with appendices by Alexander Tsymbaliuk and Alex Weekes)
• The $R$-matrix presentation for the Yangian of a simple Lie algebra
• Spinorial R operator and Algebraic Bethe Ansatz
• Vertex Representations for Yangians of Kac-Moody algebras
• Bethe subalgebras in Yangians and the wonderful compactification
• Yangian doubles of classical types and their vertex representations
• A Drinfeld-type presentation of the orthosymplectic Yangians
• Representations of the Yangians associated with Lie superalgebras $\mathfrak{osp}(1|2n)$
• Representations of the orthosymplectic Yangian
• The formal shift operator on the Yangian double
• Yangians and Baxter's relations
• Poles of finite-dimensional representations of Yangians
• The meromorphic R-matrix of the Yangian
• Transfer matrices of rational spin chains via novel BGG-type resolutions
• Orthogonal and symplectic Yangians - linear and quadratic evaluations
• Representations of Quantum Affine Algebras in their $R$-Matrix Realization
• Theta series for quantum loop algebras and Yangians
• R-Matrix presentation of quantum affine algebra in type $A_{2n-1}^{(2)}$
• The restricted quantum double of the Yangian
• On a conjecture of Khoroshkin and Tolstoy
• Yangians vs minimal W-algebras: a surprizing coincidence
• Representations of orthogonal and symplectic Yangians