A Combinatorial Study on Quiver Varieties

Research paper by Shigeyuki Fujii, Satoshi Minabe

Indexed on: 18 Nov '05Published on: 18 Nov '05Published in: Mathematics - Algebraic Geometry


This is an expository paper which has two parts. In the first part, we study quiver varieties of affine A-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating function of Poincare polynomials of quiver varieties in rank 1 cases. Our main tools are cores and quotients of Young diagrams. In the second part, we give a brief survey of instanton counting in physics, where quiver varieties appear as moduli spaces of instantons. We discuss combinatorial aspects of its recent developments.