TY - JOUR
T1 - Presentation of rational Schur algebras
AU - Marko, František
N1 - Publisher Copyright:
© 2024 Elsevier Inc.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - 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.
AB - 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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U2 - 10.1016/j.jalgebra.2024.06.044
DO - 10.1016/j.jalgebra.2024.06.044
M3 - Article
AN - SCOPUS:85202770099
SN - 0021-8693
VL - 661
SP - 904
EP - 929
JO - Journal of Algebra
JF - Journal of Algebra
ER -