Shifted twisted Yangians and Slodowy slices in classical lie algebras

Abstract In this paper we introduce the shifted twisted Yangian of type 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 gl n $\mathfrak {gl}_n$ German gl Subscript n . We deduce that these shifted twisted Yangians admit truncations which are isomorphic to Slodowy slices for many nonrectangular nilpotent elements in types B , C , 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 A . Finally we give Poisson presentations of Slodowy slices for all even nilpotent elements in types B , C , D , generalising the recent work of the second author.