Here we show that, given a finite homological system $({ \cal P},\leq,\{ \Delta_u\}_{ u\in { \cal P}})$ for a finite-dimensional algebra $\Lambda$ over an algebraically closed field, the category ${ \cal F}(\Delta)$ of $\Delta$-filtered modules is tame if and only if, for any $d\in \mathbb{ N}$, there are only finitely many isomorphism classes of generic $\Lambda$-modules adapted to ${ \cal F}(\Delta)$ with endolength $d$. We study the relationship between these generic modules and one-parameter families of indecomposables in ${ \cal F}(\Delta)$. This study applies in particular to the category of modules filtered by standard modules for standardly stratified algebras. This article includes a correction of an error in [8].
Categories: math.RT