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arXiv · 1702.08060

Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology

Giovanni Felder·Richárd Rimányi·Alexander Varchenko
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Abstract

We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and Okounkov and is based on weight functions and shuffle products. We construct an action of the dynamical elliptic quantum group associated with $\mathfrak{gl}_2$ on the equivariant elliptic cohomology of the union of cotangent bundles of Grassmannians. The generators of the elliptic quantum groups act as difference operators on sections of admissible bundles, a notion introduced in this paper.

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Giovanni Felder, Richárd Rimányi, Alexander Varchenko. 2017-02-26. Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology. https://doi.org/10.3842/sigma.2018.132

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