Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology
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 acti...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209872 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology / G. Felder, R. Rimányi, A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862642885888835584 |
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| author | Felder, G. Rimányi, R. Varchenko, A. |
| author_facet | Felder, G. Rimányi, R. Varchenko, A. |
| citation_txt | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology / G. Felder, R. Rimányi, A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 gl₂ 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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| first_indexed | 2025-12-07T14:19:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209872 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T14:19:51Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Felder, G. Rimányi, R. Varchenko, A. 2025-11-28T09:37:18Z 2018 Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology / G. Felder, R. Rimányi, A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B37; 55N34; 32C35; 55R40 arXiv: 1702.08060 https://nasplib.isofts.kiev.ua/handle/123456789/209872 https://doi.org/10.3842/SIGMA.2018.132 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 gl₂ 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. We thank Nora Ganter and Mikhail Kapranov for explanations on equivariant elliptic cohomology. G.F. was supported in part by the National Centre of Competence in Research "SwissMAP - The Mathematics of Physics" of the Swiss National Science Foundation. R.R. was supported by the Simons Foundation grant #523882. A.V. was supported in part by NSF grant DMS-1362924 and Simons Foundation grant #336826. We thank the Forschungsinstitut für Mathematik at ETH Zürich and the Max-Planck-Institut für Mathematik, Bonn, where part of this work was done, for hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology Article published earlier |
| spellingShingle | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology Felder, G. Rimányi, R. Varchenko, A. |
| title | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology |
| title_full | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology |
| title_fullStr | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology |
| title_full_unstemmed | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology |
| title_short | Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology |
| title_sort | elliptic dynamical quantum groups and equivariant elliptic cohomology |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209872 |
| work_keys_str_mv | AT felderg ellipticdynamicalquantumgroupsandequivariantellipticcohomology AT rimanyir ellipticdynamicalquantumgroupsandequivariantellipticcohomology AT varchenkoa ellipticdynamicalquantumgroupsandequivariantellipticcohomology |