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.
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Presented by: Michel Brion
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Dent, A., Tange, R. Bases for Spaces of Highest Weight Vectors in Arbitrary Characteristic. Algebr Represent Theor 22, 1133–1147 (2019). https://doi.org/10.1007/s10468-018-9815-3
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DOI: https://doi.org/10.1007/s10468-018-9815-3