The Howe duality and Lie superalgebras

Details The Howe duality and Lie superalgebras The Howe duality and Lie superalgebras

2002-02-18

arxiv.org/abs/math/0202181v1

S. Duplij and J. Wess (eds.) Noncommutative structures in mathematics and physics. Proc. NATO Advanced Research Workshop, Kiev

Mathematics

Representation Theory

27 p., Latex

Scientific paper

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 M\"obius bundle).

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