Hall polynomials for tame type

Bangming Deng Tsinghua University Shiquan Ruan Tsinghua University

Rings and Algebras mathscidoc: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
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@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.
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