Quiver varieties, affine Lie algebras, algebras of BPS states, and   semicanonical basis
  We suggest a (conjectural) construction of a basis in the plus part of the affine Lie algebra of type ADE indexed by irreducible components of certain quiver varieties. This construction is closely related to a string-theoretic construction of a Lie algebra of BPS states. We then study the new combinatorial questions about the (classical) root systems naturally arising from our constructions and Lusztig's semicanonical basis. 
Igor Frenkel, Anton Malkin, and Maxim Vybornov