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A Combinatorial Study on Quiver Varieties

Shigeyuki Fujii·Satoshi Minabe
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Abstract

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 Poincar\'e 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.

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Shigeyuki Fujii, Satoshi Minabe. 2005-10-21. A Combinatorial Study on Quiver Varieties. https://doi.org/10.3842/sigma.2017.052

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