Related Geometry

Konno, Hitoshi

doi:10.1007/978-981-15-7387-3_9

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2020

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“…We will show that these coincide with the elliptic stable envelope of X. For a further discussion of elliptic weight functions and their relation to stable envelopes in the case of the cotangent bundle of the Grassmannian, see [8].…”

Section: Definitionsmentioning

confidence: 80%

3d mirror symmetry of the cotangent bundle of the full flag variety

Dinkins¹

2020

Preprint

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Aganagic and Okounkov proved that the elliptic stable envelope provides the pole cancellation matrix for the enumerative invariants of quiver varieties known as vertex functions. This transforms a basis of a system of q-difference equations holomorphic in z with poles in a to a basis of solutions holomorphic in a with poles in z. The resulting functions are expected to be the vertex functions of the 3d mirror dual variety. In this paper, we prove that for the cotangent bundle of the full flag variety, the functions obtained in this way recover the vertex functions for the same variety under an exchange of the parameters a ↔ z. As a corollary of this, we deduce the expected 3d mirror relationship for the elliptic stable envelope.

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Section: Definitionsmentioning

confidence: 80%