# Principal W-algebras for GL(m|n)

@inproceedings{Brown2012PrincipalWF, title={Principal W-algebras for GL(m|n)}, author={Jonathan Brown and Jonathan Brundan and Simon M. Goodwin}, year={2012} }

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.

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## On the finite W-algebra for the Lie superalgebra Q(N) in the non-regular case

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## Quadratic superalgebras in mathematics and physics

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## Finite W-superalgebras for basic Lie superalgebras

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## SHIFTED YANGIANS AND FINITE W -ALGEBRAS

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## Highest Weight Theory for Finite W-Algebras

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