  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.
