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

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.

arXiv comment67 pages

References in corpus (2)

• 2-Kac-Moody algebras
• Hall polynomials for affine quivers

Cited by in corpus (1)

• On purity theorem of Lusztig's perverse sheaves