PreprintQuiver Schur algebras for the linear quiver IJun Hu and Andrew MathasAbstractWe define a graded quasihereditary covering for the cyclotomic quiver Hecke algebras \(\mathcal{R}^\Lambda_n\) of type \(A\) when \(e=0\) (the linear quiver) or \(e\ge n\). We show that these algebras are quasihereditary 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 \(\mathcal O^\Lambda_n\) 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 LLTlike algorithm for computing the graded decomposition numbers of the quiver Schur algebras in characteristic zero when \(e=0\). Keywords: Cyclotomic Hecke algebras, Schur algebras, quasihereditary and graded cellular algebras, KhovanovLaudaRouquier algebras.AMS Subject Classification: Primary 20C08; secondary 20C30, 05E10.
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