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.
Keywords
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}
}
Comments
67 pages