Integral Schur algebras for \(GL_ 2\) (Q1197382)

The structure of Schur algebras \({\mathcal S}(2,r)\) over the integral domain \(\mathbb{Z}\) is intensively studied from the quasi-hereditary algebra point of view. We introduce certain new bases for \({\mathcal S}(2,r)\) and show that the Schur algebra \({\mathcal S}(2,r)\) modulo any ideal in the defining sequence is still such a Schur algebra of lower degree in \(r\). A Wedderburn-Artin decomposition of \(S_ K(2,r)\) over a field \(K\) of characteristic 0 is described. Finally, we investigate the extension groups between two Weyl modules and classify the indecomposable Weyl- filtered modules for the Schur algebras \({\mathcal S}_{\mathbb{Z}_ p}(2,r)\) with \(r < p^ 2\).