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arXiv · 1902.03677

3d Mirror Symmetry and Elliptic Stable Envelopes

Richárd Rimányi·Andrey Smirnov·Alexander Varchenko·Zijun Zhou
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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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Richárd Rimányi, Andrey Smirnov, Alexander Varchenko, Zijun Zhou. 2019-02-10. 3d Mirror Symmetry and Elliptic Stable Envelopes. https://arxiv.org/abs/1902.03677

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