On shifted super Yangians and a class of finite W-superalgebras

Abstract

We study the finite W-superalgebra $W_e$ associated to a nilpotent element $e$ in a general linear Lie superalgebra. Under certain restriction on the Jordan type of $e$, we give a realization of $W_e$ in terms of a quotient of a shifted super Yangian.

40 pages, the title is slightly modified from the last version, to appear in Journal of Algebra. arXiv admin note: text overlap with arXiv:math/0407012 by other authors

References in corpus (5)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Principal W-algebras for GL(m|n)
• Shifted Yangians and finite W-algebras
• Finite W-superalgebras and truncated super Yangians
• Finite W-algebras

Cited by in corpus (6)

• Cohomological Hall algebras, vertex algebras and instantons
• Finite W-superalgebras via super Yangians
• Parabolic presentations of the super Yangian $Y({\mathfrak{gl}}_{M|N})$ associated with arbitrary 01-sequences
• On the finite $W$-algebra for the Lie superalgebra Q(N) in the non-regular case
• Minimal W-superalgebras and modular representations of basic Lie superalgebras
• Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras