Algebra & Number Theory

Principal $W$-algebras for $\operatorname{GL}(m\vert n)$

Jonathan Brown, Jonathan Brundan, and Simon Goodwin

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We consider the (finite) W-algebra Wm|n attached to the principal nilpotent orbit in the general linear Lie superalgebra glm|n(). Our main result gives an explicit description of Wm|n as a certain truncation of a shifted version of the Yangian Y(gl1|1). We also show that Wm|n admits a triangular decomposition and construct its irreducible representations.

Article information

Algebra Number Theory, Volume 7, Number 8 (2013), 1849-1882.

Received: 10 May 2012
Accepted: 17 December 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B10: Representations, algebraic theory (weights)
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

$W$-algebras Lie superalgebras


Brown, Jonathan; Brundan, Jonathan; Goodwin, Simon. Principal $W$-algebras for $\operatorname{GL}(m\vert n)$. Algebra Number Theory 7 (2013), no. 8, 1849--1882. doi:10.2140/ant.2013.7.1849.

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