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Description

We define a notion of slant sum of quiver gauge theories, a type of surgery on the underlying quiver. Under some mild assumptions, we relate torus fixed points on the corresponding Higgs branches, which are Nakajima quiver varieties. Then we prove a formula relating the quasimap vertex functions before and after a slant sum, which is a type of "branching rule" for vertex functions. Our construction is motivated by a conjecture, which we make here, for the factorization of the vertex functions of zero-dimensional quiver varieties, which is conjecturally related to tangent weights on the 3d mirror dual. The branching rule allows this conjecture to be approached inductively, using previously known cases as "base cases." Time permitting, we will discuss other interactions of our construction with 3dms, providing formulas for graded traces and character formulas of certain modules associated to the Coulomb branch. Joint work with Hunter Dinkins and Vasily Krylov.