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arXiv · 1212.5832

Kac's conjecture and the algebra of BPS states

Tim Cramer
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Abstract

Let Q be an affine quiver and let $\mathfrak{n}$ be the positive part of the affine Lie algebra associated to Q. We provide a construction of $\mathfrak{n}$ using the semistable irreducible components in the Lusztig nilpotent variety associated to Q. This confirms a conjecture of Frenkel, Malkin, and Vybornov on defining the so-called algebra of BPS states on the minimal resolution of a Kleinian singularity. Using the results of Crawley-Boevey and Van den Bergh, we show that our construction is closely connected to Kac's constant term conjecture in the case of an affine quiver.

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Tim Cramer. 2013-01-08. Kac's conjecture and the algebra of BPS states. https://arxiv.org/abs/1212.5832

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