%0 Journal Article
%T A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products
%A Igor Frenkel
%A Mikhail Khovanov
%A Catharina Stroppel
%J Mathematics
%D 2005
%I arXiv
%X The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra gl(n). For the special case of simple modules we naturally deduce a categorification via modules over the cohomology ring of certain flag varieties. Further geometric categorifications and the relation to Steinberg varieties are discussed. We also give a categorical version of the quantised Schur-Weyl duality and an interpretation of the (dual) canonical bases and the (dual) standard bases in terms of projective, tilting, standard and simple Harish-Chandra bimodules.
%U http://arxiv.org/abs/math/0511467v1