Kac's conjecture and the algebra of BPS states

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