Quiver varieties, affine Lie algebras, algebras of BPS states, and semicanonical basis

Frenkel, Igor; Malkin, Anton; Vybornov, Maxim

Quiver varieties, affine Lie algebras, algebras of BPS states, and semicanonical basis

Authors

Frenkel, Igor

Malkin, Anton

Vybornov, Maxim

Description

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.
16 pages