Quiver Schur algebras I: linear quivers

Details Quiver Schur algebras I: linear quivers Quiver Schur algebras I: linear quivers

2011-10-08

arxiv.org/abs/1110.1699v2

Mathematics

Representation Theory

Title changed. References and appendix on level 2 case added

Scientific paper

We define a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras $\R$ of type $A$ when $e=0$ (the linear quiver) or $e\ge n$. We show that these algebras are quasi-hereditary graded cellular algebras by giving explicit homogeneous bases for them. When $e=0$ we show that the KLR grading on the quiver Hecke algebras is compatible with the gradings on parabolic category $\O$ previously introduced in the works of Beilinson, Ginzburg and Soergel and Backelin. As a consequence, we show that when $e=0$ our graded Schur algebras are Koszul over field of characteristic zero. Finally, we give an LLT-like algorithm for computing the graded decomposition numbers of the quiver Schur algebras in characteristic zero when $e=0$.

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