Principal W-algebras for GL(m|n)

Brown, Jonathan; Brundan, Jonathan; Goodwin, Simon

doi:10.2140/ant.2013.7.1849

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

Jonathan Brown, Jonathan Brundan and Simon M. Goodwin

Vol. 7 (2013), No. 8, 1849–1882

DOI: 10.2140/ant.2013.7.1849

Abstract

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

Keywords

$W$-algebras, Lie superalgebras

Mathematical Subject Classification 2010

Primary: 17B10

Secondary: 17B37

Milestones

Received: 10 May 2012

Accepted: 17 December 2012

Published: 24 November 2013

Authors

Jonathan Brown
Department of Mathematics, Computer Science, and Statistics State University of New York College at Oneonta Oneonta, NY 13820 United States

Jonathan Brundan
Department of Mathematics University of Oregon Eugene, OR 97403 United States

Simon M. Goodwin
School of Mathematics University of Birmingham Birmingham B15 2TT United Kingdom

Vol. 7, No. 8, 2013