Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula

Jie Xiao Tsinghua University Fan Xu Tsinghua University Minghui Zhao Beijing Forestry University

Quantum Algebra Representation Theory mathscidoc:1610.29001

In this paper, we generalize the categorifical construction of a quantum group and its canonical basis by Lusztig (\cite{Lusztig,Lusztig2}) to the generic form of whole Ringel-Hall algebra. We clarify the explicit relation between the Green formula in \cite{Green} and the restriction functor in \cite{Lusztig2}. By a geometric way to prove Green formula, we show that the Hopf structure of a Ringel-Hall algebra can be categorified under Lusztig's framework.
Hall algebra, induction functor, restriction functor, simple perverse sheaves
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@inproceedings{jieringel-hall,
  title={Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula},
  author={Jie Xiao, Fan Xu, and Minghui Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161004104503327117083},
}
Jie Xiao, Fan Xu, and Minghui Zhao. Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161004104503327117083.
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