【59页精品】Quiver Schur algebras I: linear quivers

Abstract: We define a graded quasi-hereditary covering for the cyclotomic quiver Heckealgebras $\R$ of type $A$ when $e=0$ (the linear quiver) or $e\ge n$. We showthat these algebras are quasi-hereditary graded cellular algebras by givingexplicit homogeneous bases for them. When $e=0$ we show that the KLR grading onthe quiver Hecke algebras is compatible wi..