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Algebras and Representation Theory

, Volume 22, Issue 5, pp 1133–1147 | Cite as

Bases for Spaces of Highest Weight Vectors in Arbitrary Characteristic

  • Adam Dent
  • Rudolf TangeEmail author
Open Access
Article
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Abstract

Let k be an algebraically closed field of arbitrary characteristic. First we give explicit bases for the highest weight vectors for the action of GLr ×GLs on the coordinate ring \(k[\text {Mat}_{rs}^{m}]\) of m-tuples of r × s-matrices. It turns out that this is done most conveniently by giving an explicit good GLr ×GLs-filtration on \(k[\text {Mat}_{rs}^{m}]\). Then we deduce from this result explicit spanning sets of the \(k[\text {Mat}_{n}]^{\text {GL}_{n}}\)-modules of highest weight vectors in the coordinate ring k[Matn] under the conjugation action of GLn.

Keywords

Highest weight vector 

Mathematics Subject Classification (2010)

13A50 16W22 20G05 

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK

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