Bows, Instantons, and Representations of Affine Kac-Moody Algebras.

Kronheimer and Nakajima constructed Yang-Mills instantons on orbifolds of the euclidean four-space in terms of quivers. The moduli spaces of such instantons are called quiver varieties. Nakajima also identified an action of an affine Kac-Moody algebra on the cohomology of quiver varieties. Frenkel’s level-rank duality gives a different affine Kac-Moody algebra action on these spaces.

We generalize the construction of Kronheimer and Nakajima to Yang-Mills instantons on a larger class of spaces. Our construction is formulated in terms of bows. The resulting moduli spaces of such instantons, or bow varieties, are richer with larger cohomology spaces. We address the question representation theoretic interpretation of these spaces.