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Flags of sheaves, quivers and symmetric polynomials (1911.12787v2)

Published 28 Nov 2019 in math.AG and hep-th

Abstract: We study the representation theory of the nested instantons quiver presented in [1], which describes a particular class of surface defects in four-dimensional supersymmetric gauge theories. We show that the moduli space of its stable representations provides an ADHM-like construction for nested Hilbert schemes of points on $\mathbb C2$, for rank one, and for the moduli space of flags of framed torsion-free sheaves on $\mathbb P2$, for higher rank. We introduce a natural torus action on this moduli space and use equivariant localization to compute some of its (virtual) topological invariants, including the case of compact toric surfaces. We conjecture that the generating function of holomorphic Euler characteristics for rank one is given in terms of polynomials in the equivariant weights, which, for specific numerical types, coincide with (modified) Macdonald polynomials.

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