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Bases for fixed points of unipotent elements acting on the tensor square and the spaces of alternating and symmetric 2-tensors

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Author(s)
Barry, Michael J. J.
Date Issued
May 2002
Abstract
If V is a vector space over a field K, then an element g of the general linear group GL(V) acts on V ⊗ 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 ⊗ V and A(V) which are valid for every field K, and a basis for the subspace of fixed points of g acting on S(V) which is valid for every field K with char K ≠ 2.
Journal
Journal of Algebra
Department
Mathematics
Citation
Barry, M.J.J. (2002). Bases for fixed points of unipotent elements acting on the tensor square and the spaces of alternating and symmetric 2-tensors. Journal of Algebra, 251: 395-412. doi: 10.1006/jabr.2001.9149
Publisher
Elsevier
Version of Article
Published article
DOI
10.1006/jabr.2001.9149
ISSN
0021-8693
Rights
This article was selected and published in the Journal of Algebra ©2002 Barry. All rights reserved.
Subjects

tensor product

exterior product

symmetric product

unipotent action

bases of fixed spaces...

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