Schurifying quasi-hereditary algebras
Proceedings of the London Mathematical Society
We study new classes of quasi-hereditary and cellular algebras which generalize Turner's double algebras. Turner's algebras provide a local description of blocks of symmetric groups up to derived equivalence. Our general construction allows one to “schurify” any quasi-hereditary algebra (Formula presented.) to obtain a generalized Schur algebra (Formula presented.) which we prove is again quasi-hereditary if (Formula presented.). We describe decomposition numbers of (Formula presented.) in terms of those of (Formula presented.) and the classical Schur algebra (Formula presented.). In fact, it is essential to work with quasi-hereditary superalgebras (Formula presented.), in which case the construction of the schurification involves a non-trivial full rank sub-lattice (Formula presented.).
Kleshchev, A., & Muth, R. (2022). Schurifying quasi-hereditary algebras. Proceedings of the London Mathematical Society. https://doi.org/10.1112/plms.12466