Principal W-algebras for GL(m|n)

Jonathan Brown; Jonathan Brundan; Simon M. Goodwin

doi:10.2140/ant.2013.7.1849

Principal W-algebras for GL(m|n)

Jonathan Brown, Jonathan Brundan, Simon M. Goodwin

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

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(ℂ). 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.

Original language	English
Pages (from-to)	1849-1882
Number of pages	34
Journal	Algebra and Number Theory
Volume	7
Issue number	8
DOIs	https://doi.org/10.2140/ant.2013.7.1849
Publication status	Published - 2013

Keywords

Lie superalgebras
W-algebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.2140/ant.2013.7.1849

Representation Theory of Finite W-algebras
Goodwin, S.
Engineering & Physical Science Research Council
17/08/09 → 16/08/12
Project: Research Councils

Cite this

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AB - We consider the (finite) W-algebra Wm|n attached to the principal nilpotent orbit in the general linear Lie superalgebra glm|n(ℂ). 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.

KW - Lie superalgebras

KW - W-algebras

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Principal W-algebras for GL(m|n)

Abstract

Keywords

ASJC Scopus subject areas

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Projects

Representation Theory of Finite W-algebras

Cite this