The exterior algebra and `Spin' of an orthogonal g-module

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dc.creatorPanyushev, Dmitri I.
dc.date2000-01-28
dc.date.accessioned2026-07-07T04:33:27Z
dc.date.available2026-07-07T04:33:27Z
dc.descriptionA well-known result of Kostant gives a description of the G-module structure for the exterior algebra of Lie algebra $\frak g$. We give a generalization of this result for the isotropy representations of symmetric spaces. If $\frak g={\frak g}_0+{\frak g_1}$ is a Z_2-grading of a simple Lie algebra, we explicitly describe a ${\frak g}_0$-module $Spin_0({\frak g}_1)$ such that the exterior algebra of ${\frak g}_1$ is the tensor square of this module times some power of 2. Although $Spin_0({\frak g}_1)$ is usually reducible, we show that a Casimir element for ${\frak g}_0$ always acts scalarly on it. We also a give classification of all orthogonal representations of simple algebraic groups having an exterior algebra of skew-invariants.
dc.descriptionLaTeX 2.09, 30 pages
dc.identifierhttps://arxiv.org/abs/math/0001161
dc.identifierhttp://arxiv.org/abs/math/0001161
dc.identifierTransformation Groups, 6 (2001), 371-396
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58583
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.titleThe exterior algebra and `Spin' of an orthogonal g-module
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