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arXiv · 2307.15628

Presentation of rational Schur algebras

František Marko
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Abstract

We present rational Schur algebra $S(n,r,s)$ over an arbitrary ground field $K$ as a quotient of the distribution algebra $Dist(G)$ of the general linear group $G=GL(n)$ by an ideal $I(n,r,s)$ and provide an explicit description of the generators of $I(n,r,s)$. Over fields $K$ of characteristic zero, this corrects and completes a presentation of $S(n,r,s)$ 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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František Marko. 2024-04-29. Presentation of rational Schur algebras. https://arxiv.org/abs/2307.15628

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