Bangming DengTsinghua UniversityShiquan RuanTsinghua University
Rings and Algebrasmathscidoc:1610.31001
In the present paper we prove that Hall polynomial exists for each triple of decomposition
sequences which parameterize isomorphism classes of coherent sheaves of a domestic weighted projective
line $\mathbb X$ over finite fields. These polynomials are then used to define the generic Ringel--Hall
algebra of $\mathbb X$ as well as its Drinfeld double. Combining this construction with a result of Cramer,
we show that Hall polynomials exist for tame quivers, which not only refines a result of Hubery, but also
confirms a conjecture of Berenstein and Greenstein.
weighted projective line, Hall polynomial, Ringel-Hall algebra, Green's formula
@inproceedings{bangminghall,
title={Hall polynomials for tame type},
author={Bangming Deng, and Shiquan Ruan},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161006200815924360092},
}
Bangming Deng, and Shiquan Ruan. Hall polynomials for tame type. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161006200815924360092.