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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2002-05
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Barry, Michael J. J.
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Keywords
tensor product , exterior product , symmetric product , unipotent action , bases of fixed spaces
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.
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Mathematics
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This article was selected and published in the Journal of Algebra ©2002 Barry. All rights reserved.
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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
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Elsevier
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