Mathematics – Algebraic Geometry
Scientific paper
2000-01-28
Transformation Groups, 6 (2001), 371-396
Mathematics
Algebraic Geometry
LaTeX 2.09, 30 pages
Scientific paper
A 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.
No associations
LandOfFree
The exterior algebra and `Spin' of an orthogonal g-module does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The exterior algebra and `Spin' of an orthogonal g-module, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The exterior algebra and `Spin' of an orthogonal g-module will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-336494