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Stabilizers of the GL-action on tensor and symmetric powers

โœ Scribed by Francisco Guil-Asensio; Manuel Saorin

Publisher
Elsevier Science
Year
2000
Tongue
French
Weight
63 KB
Volume
124
Category
Article
ISSN
0007-4497

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โœฆ Synopsis

We fix a finite dimensional vector space and a basis B of V and completely identify the identity component of the stabilizer, under diagonal action by GL(V ), of every subspace of a direct sum of tensor or symmetric powers of V that is generated by powers of elements of B.

๐Ÿ“œ SIMILAR VOLUMES

Bases for Fixed Points of Unipotent Elem
Bases for Fixed Points of Unipotent Elements Acting on the Tensor Square and the Spaces of Alternating and Symmetric 2-Tensors
โœ Michael J.J. Barry ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 128 KB

If V is a vector space over a field K, then an element g of the general linear group GL V acts on V โŠ— V , on the space of alternating 2-tensors A V , and on the space of symmetric 2-tensors S V . For a unipotent element g, we exhibit bases for the subspace of fixed points of g acting on both V โŠ— V a