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This article is cited in 12 scientific papers (total in 12 papers)
Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology
Giovanni Feldera, Richárd Rimányib, Alexander Varchenkob a Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
b Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA
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.
Keywords:
elliptic cohomology; elliptic quantum group; elliptic stable envelope.
Received: April 30, 2018; in final form December 12, 2018; Published online December 21, 2018
Citation:
Giovanni Felder, Richárd Rimányi, Alexander Varchenko, “Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology”, SIGMA, 14 (2018), 132, 41 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1431 https://www.mathnet.ru/eng/sigma/v14/p132
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Abstract page: | 138 | Full-text PDF : | 25 | References: | 15 |
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