Remarks on PBW bases of Ringel-Hall algebras of cyclic quivers
Abstract
In this paper, we give a recursive formula for the interesting PBW basis EA of composition subalgebras of Ringel-Hall algebras (n) of cyclic quivers after DengDuXiao2007generic, and another construction of canonical bases of v+(n) from the monomial bases m(A) follow DuZhaomultiplication. As an application, we will determined all the canonical basis of v+(2) associated with modules of Lowery length ≤s3. Finally, we will discuss the relation of canonical bases of Ringel-Hall algebras and those of affine quantum Schur algebras.
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