Tilting, deformations and representations of linear groups over Euclidean algebras

Abstract

We study irreducible unitary representations of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of a Dynkin or Euclidean quiver. In particular, we describe such generic representations: we prove that there exists an open dense subset of the space of irreducible unitary representations isomorphic to the product of dual spaces of full linear groups and, perhaps, one more (explicitly described) space. The proof uses the technique of bimodule categories, deformations and representations of quivers.