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

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.

preprint2015arXivOpen access
Guanglian Zhang
math.RTmath.AG
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Guanglian Zhang

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