Hall polynomials for tame type

Bangming Deng; Shiquan Ruan

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arXiv · 1512.03504

Hall polynomials for tame type

Bangming Deng·Shiquan Ruan

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Abstract

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.

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Bangming Deng, Shiquan Ruan. 2015-12-11. Hall polynomials for tame type. https://arxiv.org/abs/1512.03504

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