Bases for Fixed Points of Unipotent Elements Acting on the Tensor Square and the Spaces of Alternating and Symmetric 2-Tensors

✍ Scribed by Michael J.J. Barry

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 128 KB
• Volume: 251
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.9149

✦ Synopsis

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.  2002 Elsevier Science (USA)