A Combinatorial Study on Quiver Varieties

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 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.

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Cited by in corpus (19)

• Fivebranes and 3-manifold homology
• Counting Chiral Operators in Quiver Gauge Theories
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Instantons on ALE spaces and orbifold partitions
• Coset conformal blocks and N=2 gauge theories
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• Amoebas and Instantons
• N=2 quiver gauge theories on A-type ALE spaces
• Coset conformal field theory and instanton counting on C^2/Z_p
• Crystal melting on toric surfaces
• Plethystics and instantons on ALE spaces
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Double Quiver Gauge Theory and BPS/CFT Correspondence
• Combinatorial realizations of crystals via torus actions on quiver varieties
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Twisted Representations of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal Blocks
• Enumerating coloured partitions in 2 and 3 dimensions
• Notes On U(1) Instanton Counting On $A_{l-1}$ ALE Spaces