Bases for spaces of highest weight vectors in arbitrary characteristic
Representation Theory
2018-01-26 v2
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 GL_r x GL_s on the coordinate ring k[Mat_{rs}^m] of m-tuples of r x s-matrices. It turns out that this is done most conveniently by giving an explicit good GL_r x GL_s-filtration on k[Mat_{rs}^m]. Then we deduce from this result explicit spanning sets of the k[Mat_n]^{GL_n}-modules of highest weight vectors in the coordinate ring k[Mat_n] under the conjugation action of GL_n.
Keywords
Cite
@article{arxiv.1610.06948,
title = {Bases for spaces of highest weight vectors in arbitrary characteristic},
author = {Adam Dent and Rudolf Tange},
journal= {arXiv preprint arXiv:1610.06948},
year = {2018}
}