Finite W-superalgebras via super Yangians

Abstract

Let $e$ be an arbitrary even nilpotent element in the general linear Lie superalgebra ${\mathfrak{gl}}_{M|N}$ and let ${\mathcal{W}}_e$ be the associated finite $W$-superalgebra. Let $Y_{m|n}$ be the super Yangian associated to the Lie superalgebra ${\mathfrak{gl}}_{m|n}$. A subalgebra of $Y_{m|n}$, called the shifted super Yangian and denoted by $Y_{m|n}(\sigma )$, is defined and studied. Moreover, an explicit isomorphism between ${\mathcal{W}}_e$ and a quotient of $Y_{m|n}(\sigma )$ is established.

56 pages, version 2, comments welcome. Minor revision, added one section and fixed some typos

References in corpus (3)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• On the finite $W$-algebra for the Lie superalgebra Q(N) in the non-regular case
• Lax matrices from antidominantly shifted Yangians and quantum affine algebras: A-type

Cited by in corpus (5)

• Affine Super Yangians and Rectangular $W$-superalgebras
• A note on odd reflections of super Yangian and Bethe ansatz
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• On finite dimensional representations of finite W-superalgebras
• Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras