The Howe duality and Lie superalgebras

2002/02/18 by Dimitry Leites, Irina Shchepochkina
Mathematics · #math.RT #msc:22E45 #msc:17B #msc:11E57 #msc:15A72 #msc:20G05 #msc:22E47

paper · pdf

published as S. Duplij and J. Wess (eds.) Noncommutative structures in mathematics and physics. Proc. NATO Advanced Research Workshop, Kiev, 2000. Kluwer, 93-111 · 27 p., Latex

arxiv created 2002/02/18 · arxiv updated 2009/11/30

Abstract

Howe's duality is considered from a unifying point of view based on Lie superalgebras. New examples are offered. In particular, we construct several simplest spinor-oscillator representations and compute their highest weights for the 'stringy' Lie superalgebras (i.e., Lie superalgebras of complex vector fields (or their nontrivial central extensions) on the supercircle S^1|n and its two-sheeted cover associated with the Möbius bundle).

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