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The Howe duality and Lie superalgebras

Dimitry Leites·Irina Shchepochkina
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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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Dimitry Leites, Irina Shchepochkina. 2002-02-18. The Howe duality and Lie superalgebras. https://arxiv.org/abs/math/0202181

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