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

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

Access to Document

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

@article{b3db242dd2c94d37903715dc2d083b08,

title = "Principal W-algebras for GL(m|n)",

abstract = "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.",

keywords = "Lie superalgebras, W-algebras",

author = "Jonathan Brown and Jonathan Brundan and Goodwin, {Simon M.}",

year = "2013",

doi = "10.2140/ant.2013.7.1849",

language = "English",

volume = "7",

pages = "1849--1882",

journal = "Algebra and Number Theory",

issn = "1937-0652",

publisher = "Mathematical Sciences Publishers",

number = "8",

}

TY - JOUR

T1 - Principal W-algebras for GL(m|n)

AU - Brown, Jonathan

AU - Brundan, Jonathan

AU - Goodwin, Simon M.

PY - 2013

Y1 - 2013

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84888997212&partnerID=8YFLogxK

U2 - 10.2140/ant.2013.7.1849

DO - 10.2140/ant.2013.7.1849

M3 - Article

AN - SCOPUS:84888997212

SN - 1937-0652

VL - 7

SP - 1849

EP - 1882

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 8

ER -

Principal W-algebras for GL(m|n)

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Projects

Representation Theory of Finite W-algebras

Cite this