Remarks on PBW bases of Ringel-Hall algebras of cyclic quivers

2016/08/22 by Zhao, Zhonghua
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1608.06062

Abstract

In this paper, we give a recursive formula for the interesting PBW basis E_A of composition subalgebras of Ringel-Hall algebras \fkH_\vartri(n) of cyclic quivers after \citeDengDuXiao2007generic, and another construction of canonical bases of \U_v⁺(\wih\fks\fkl_n) from the monomial bases m^(A) follow \citeDuZhaomultiplication. As an application, we will determined all the canonical basis of \U_v⁺(\wih\fks\fkl₂) associated with modules of Lowery length \leqs3. Finally, we will discuss the relation of canonical bases of Ringel-Hall algebras and those of affine quantum Schur algebras.

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