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arXiv · 2406.05492

Shifted twisted Yangians and Slodowy slices in classical Lie algebras

Lukas Tappeiner·Lewis Topley
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Abstract

In this paper we introduce the shifted twisted Yangian of type {\sf AI}, following the work of Lu--Wang--Zhang, and we study their semiclassical limits, a class of Poisson algebras. We demonstrate that they coincide with the Dirac reductions of the semiclassical shifted Yangian for $\mathfrak{gl}_n$. We deduce that these shifted twisted Yangians admit truncations which are isomorphic to Slodowy slices for many non-rectangular nilpotent elements in types {\sf B}, {\sf C}, {\sf D}. As a direct consequence we obtain parabolic presentations of the semiclassical shifted twisted Yangian, analogous to those introduced by Brundan--Kleshchev for the Yangian of type {\sf A}. Finally we give Poisson presentations of Slodowy slices for all even nilpotent elements in types {\sf B}, {\sf C}, {\sf D}, generalising the recent work of the second author.

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BibTeXRIS

Lukas Tappeiner, Lewis Topley. 2024-06-08. Shifted twisted Yangians and Slodowy slices in classical Lie algebras. https://arxiv.org/abs/2406.05492

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