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

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.

37 pages, a relation was missing in the previous version

References in corpus (5)

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• Highest weight theory for finite W-algebras
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