Hall polynomials for tame type
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 RingelHall 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.03504
 Bibcode:
 2015arXiv151203504D
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra
 EPrint:
 27 pages