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3d Mirror Symmetry and Elliptic Stable Envelopes
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abstract
We consider a pair of quiver varieties (X;X') related by 3d mirror symmetry, where X =T*Gr(k,n) is the cotangent bundle of the Grassmannian of k-planes of n-dimensional space. We give formulas for the elliptic stable envelopes on both sides. We show an existence of an equivariant elliptic cohomology class on X $\times$ X' (the Mother function) whose restrictions to X and X' are the elliptic stable envelopes of those varieties. This implies, that the restriction matrices of the elliptic stable envelopes for X and X' are equal after transposition and identification of the equivariant parameters on one side with the K\"ahler parameters on the dual side.
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Cited by 1 Pith paper
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Characters of tangent spaces at torus fixed points and $3d$-mirror symmetry
Conjecture 1 equates the chamber-limit vertex function of a quiver variety with a q-binomial product whose exponents are the weights of the repelling tangent subspace at the mirror fixed point.
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