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2013•Algebra & Number TheoryOpen access

PrincipalW-algebras for GL(m|n)

Jonathan Brown, Jonathan Brundan, Simon M. Goodwin

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Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Mathematics, Yangian, Lie superalgebra, Nilpotent, Truncation (statistics), Pure mathematics, Lie algebra, Algebra over a field

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