A Combinatorial Study on Quiver Varieties

Symmetry Integrability and Geometry-Methods and Applications

article

Shigeyuki Fujii¹  Satoshi Minabe² 

[1] Accenture Strategy;Department of Mathematics, Tokyo Denki University

关键词: Young diagram;    core;    quotient;    quiver variety;    instanton;   

DOI  :  10.3842/SIGMA.2017.052

来源: National Academy of Science of Ukraine

【 摘 要 】

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 Poincaré 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, focusing on its combinatorial aspects.

【 授权许可】

Unknown