Principal W-algebras for GL(m|n)

Abstract

We consider the (finite) $W$-algebra $W_{m|n}$ attached to the principal nilpotent orbit in the general linear Lie superalgebra ${\mathfrak{gl}}_{m|n}(\mathbb{C})$. Our main result gives an explicit description of $W_{m|n}$ as a certain truncation of a shifted version of the Yangian $Y({\mathfrak{gl}}_{1|1})$. We also show that $W_{m|n}$ admits a triangular decomposition and construct its irreducible representations.

This version corrects a formatting bug with txfonts package in the arxiv's tex distribution (\bar was not displayed correctly)

References in corpus (8)

• Finite vs. affine W-algebras
• Representations of shifted Yangians and finite W-algebras
• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Quantization of Slodowy slices
• Shifted Yangians and finite W-algebras
• W-superalgebras as truncation of super-Yangians
• Parabolic presentations of the super Yangian $Y(g{l}_{M|N})$
• Finite $W$-superalgebras for queer Lie superalgebras

Cited by in corpus (15)

• Finite W-superalgebras via super Yangians
• On shifted super Yangians and a class of finite W-superalgebras
• 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
• Odd reflections in the Yangian associated with $\mathfrak{g}l(m|n)$
• Minimal W-superalgebras and modular representations of basic Lie superalgebras
• Super formal Daboux-Weinstein theorem and finite W superalgebra
• Dimensions of irreducible modules over W-algebras and Goldie ranks
• Finite $W$-superalgebras and the dimensional lower bounds for the representations of basic Lie superalgebras
• Finite W-superalgebras for basic Lie superalgebras
• Finite W-superalgebras for basic classical Lie superalgebras
• On finite dimensional representations of finite W-superalgebras
• On the Premet conjecture for finite W-superalgebras
• Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras
• Finite $W$-superalgebras and quadratic spacetime supersymmetries