Generic extensions and canonical bases for cyclic quivers

Abstract

We use the monomial basis theory developed by Deng and Du to present an elementary algebraic construction of the canonical bases for both the Ringel-Hall algebra of a cyclic quiver and the positive part U+ of the quantum affine sln. This construction relies on analysis of quiver representations and the introduction of a new integral PBW-like basis for the Lusztig ℤ [ν, ν-1]-form of U+. ©Canadian Mathematical Society 2007.