A criterion for quasi-hereditary, and an abstract straightening formula
The author provides a criterion to see whether an algebra is quasi-hereditary. (Of course, this is a very interesting question.) The main point is that the criterion given by the author uses an integral version of the given algebra. Thus he imposes conditions not on the given algebra itself, but on its integral version and a certain semisimple algebra which contains the given one. The condition is, roughly speaking, a straightening formula for a formal character of the semisimple algebra. By applying his criterion to many important algebras, he gets a unified proof of the quasi-heredity of Schur algebras, generalized Schur algebras, \(q\)-Schur algebras and the Temperley-Lieb algebras of type \(A\) and \(B\) with non-zero parameters, (for these algebras, the known quasi-heredity was proved by many other authors using different methods).
scientific article; zbMATH DE number 1026421
scientific article