There are several different ways to construct affine canonical bases, in addition to approaches by Lusztig and Kashiwara. In this paper we present a different approach to canonical bases via Hall algebras and representations of tame quivers over finite fields. The main idea is to tensor together integral bases constructed for cyclic quivers and Kronecker quivers with those from the preinjective and preprojective parts of tame quiver representations. Several different bases: a PBW type basis, a monomial basis, and a barinvariant basis are constructed and their relations to the canonical basis are discussed. The result also answers a question by Nakajima.
Abstract. The notion of quantum group equivariant homogeneous vector bundles on quantum homogeneous spaces is introduced. The category of such quantum vector bundles is shown to be exact, and its Grothendieck group is determined. It is also shown that the algebras of functions on quantum homogeneous spaces are noetherian.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.