English

Canonical bases for the quantum extended Kac-Moody algebras and Hall polynomials

Representation Theory 2015-10-13 v4 Algebraic Geometry

Abstract

In this paper, the singular Ringel-Hall algebra for a tame quiver is introduced and shown to be isomorphic to the positive part of the quantum extended Kac-Moody algebra. A PBW basis is constructed and a new class of perverse sheaves is shown to have purity property. This allows to construct the canonical bases of the positive part of the quantum extended Kac-Moody algebra. As an application, the existence of Hall polynomials for tame quiver algebras is proved.

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Cite

@article{arxiv.0901.1720,
  title  = {Canonical bases for the quantum extended Kac-Moody algebras and Hall polynomials},
  author = {Guanglian Zhang},
  journal= {arXiv preprint arXiv:0901.1720},
  year   = {2015}
}

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67 pages