Vol. 7, No. 8, 2013

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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

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.

$W$-algebras, Lie superalgebras
Mathematical Subject Classification 2010
Primary: 17B10
Secondary: 17B37
Received: 10 May 2012
Accepted: 17 December 2012
Published: 24 November 2013
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