Presentation of rational Schur algebras

2023/07/28 by František Marko, Marko, František
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.15628

openalex publication_date 2023/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The rational Schur algebra
• Generalized Schur Algebras
• Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2)
• Presenting Schur Algebras
• Comparing GL_n-Representations by Characteristic-Free Isomorphisms between Generalized Schur Algebras