Dominant and global dimension of blocks of quantised Schur algebras
Schur algebras and quantised (or \(q\)-) Schur algebras have been fundamental objects in representation theory since its early days. In the paper under review, the authors give explicit formulae for the dominant and the global dimension of indecomposable blocks of \(S(n,r)\) and \(S_q(n,r)\) with \(n\geq r\). The main methods used in the proofs come from the derived equivalences constructed by the authors [J. Reine Angew. Math. 770, 59--85 (2021; Zbl 1472.18008)]. As an application, it is shown that two blocks \(B\) and \(B'\) of Schur algebras \(S_q(n,r)\) for \(n\geq r\) and \(S_q(n',r')\) for \(n'\geq r'\), respectively, are derived equivalent if and only if they have the same global dimension.
scientific article; zbMATH DE number 7463798
scientific article