Shifted twisted Yangians and even finite W-algebras (NOTE ROOM CHANGE)

Lewis Topley (University of Bath)

Wednesday 13th November 16:00-17:00 CTT 2 UNIV GDNS:209

Abstract

There is a well-known relationship between finite W-algebras and Yangians. The work of Rogoucy and Sorba on the "rectangular case" in type A eventually led Brundan and Kleshchev to introduce shifted Yangians, which surject onto the finite W-algebras for general linear Lie algebras. Thus, these W-algebras can be realised as trucated shifted Yangians. In parallel, the work of Ragoucy and then Brown showed that truncated twisted Yangians is isomorphic to the finite W-algebra associated to a rectangular nilpotent element in a Lie algebra of type B, C or D. For many years there has been a hope that this relationship can be extended to other nilpotent elements.

I will report on a joint work with Lukas Tappeiner in which we introduced the shifted twisted Yangians, following the work of Lu-Wang-Zhang, and described Poisson isomorphisms between their truncated semiclassical degenerations and the Slodowy slices associated with even nilpotent elements in classical simple Lie algebras. I will also mention a work in progress with Lu-Peng-Tappeiner-Wang which deals with the quantum analogue of our theorem.

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