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arXiv · 1601.05701

A Drinfeld presentation for the twisted Yangian $Y_3^+$

Jonathan S Brown
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Abstract

We define the Drinfeld generators for $Y_3^+$, the twisted Yangian associated to the Lie algebra $\mathfrak{so}_3(\mathbb{C})$. This allows us to define shifted twisted Yangians, which are certain subalgebras of $Y_3^+$. We show that there are families of homomorphisms from the shifted twisted Yangians in $Y_3^+$ to the universal enveloping algebras of various orthogonal and symplectic Lie algebras, and we conjecture that the images of these homomorphisms are isomorphic to various finite $W$-algebras.

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Jonathan S Brown. 2016-01-21. A Drinfeld presentation for the twisted Yangian $Y_3^+$. https://arxiv.org/abs/1601.05701

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