Presentation of rational Schur algebras
Franti\v{s}ek Marko

TL;DR
This paper provides an explicit presentation of rational Schur algebras over arbitrary fields, correcting previous work in characteristic zero and introducing the first such presentation for positive characteristic fields.
Contribution
It offers a new explicit description of the generators of the ideal defining rational Schur algebras over any ground field, including positive characteristic fields.
Findings
Explicit generators for the ideal I(n,r,s) over any field
Correction and completion of previous presentations in characteristic zero
First explicit presentation over fields of positive characteristic
Abstract
We present rational Schur algebra over an arbitrary ground field as a quotient of the distribution algebra of the general linear group by an ideal and provide an explicit description of the generators of . Over fields of characteristic zero, this corrects and completes a presentation of in terms of generators and relations originally considered by Dipper and Doty. The explicit presentation over ground fields of positive characteristics appears here for the first time.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Carbohydrate Chemistry and Synthesis
