SPP 1388 - WP: Actions of Algebraic Groups, Fans and Tilting Modules (2nd funding period)

Basic data for this project

Description

To any finite dimensional algebra of finite global dimension one can associate a fan of tilting modules of projective dimension at most one. This fan is connected for representation finite and tame hereditary algebras. Moreover, the support of the fan classifies the actions of the corresponding group on the representation space with a dense orbit. In particular, the action of a parabolic subgroup in a General Linear Group on a subideal in the Lie algebra of the unipotent radical can be described in this way.The principal aim of this project is to understand the fan for hereditary algebras, in particular its connected components. Moreover, for actions of parabolic groups the fan might be connected as well, which in turn would classify all such actions with a dense orbit. Finally, we would like to generalize the results to actions for parabolic subgroups in the classical linear algebraic groups.