{"date_created":"2025-07-10T13:31:38Z","_id":"19987","quality_controlled":"1","type":"book_chapter","status":"public","acknowledgement":"Y.Y. would like to thank the organizers of the MATRIX program Geometric R-Matrices: from Geometry to Probability for their kind invitation, and many participants of the program for useful discussions, including Vassily Gorbounov, Andrei Okounkov, Allen Knutson, Hitoshi Konno, Paul Zinn-Justin. Proposition 1 and Sect. 3.3 are new, for which we thank Hitoshi Konno for interesting discussions and communications. These notes were written when both authors were visiting the Perimeter Institute for Theoretical Physics (PI). We are grateful to PI for the hospitality.","arxiv":1,"intvolume":"         2","department":[{"_id":"TaHa"}],"publication_status":"published","doi":"10.1007/978-3-030-04161-8_54","language":[{"iso":"eng"}],"volume":2,"OA_type":"green","author":[{"last_name":"Yang","id":"360D8648-F248-11E8-B48F-1D18A9856A87","full_name":"Yang, Yaping","first_name":"Yaping"},{"id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang","last_name":"Zhao","first_name":"Gufang"}],"citation":{"mla":"Yang, Yaping, and Gufang Zhao. “How to Sheafify an Elliptic Quantum Group.” <i>2017 MATRIX Annals</i>, vol. 2, Springer International Publishing, 2019, pp. 675–91, doi:<a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">10.1007/978-3-030-04161-8_54</a>.","apa":"Yang, Y., &#38; Zhao, G. (2019). How to Sheafify an Elliptic Quantum Group. In <i>2017 MATRIX Annals</i> (Vol. 2, pp. 675–691). Cham: Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">https://doi.org/10.1007/978-3-030-04161-8_54</a>","chicago":"Yang, Yaping, and Gufang Zhao. “How to Sheafify an Elliptic Quantum Group.” In <i>2017 MATRIX Annals</i>, 2:675–91. MXBS. Cham: Springer International Publishing, 2019. <a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">https://doi.org/10.1007/978-3-030-04161-8_54</a>.","ista":"Yang Y, Zhao G. 2019.How to Sheafify an Elliptic Quantum Group. In: 2017 MATRIX Annals. MATRIX Book Series, vol. 2, 675–691.","short":"Y. Yang, G. Zhao, in:, 2017 MATRIX Annals, Springer International Publishing, Cham, 2019, pp. 675–691.","ieee":"Y. Yang and G. Zhao, “How to Sheafify an Elliptic Quantum Group,” in <i>2017 MATRIX Annals</i>, vol. 2, Cham: Springer International Publishing, 2019, pp. 675–691.","ama":"Yang Y, Zhao G. How to Sheafify an Elliptic Quantum Group. In: <i>2017 MATRIX Annals</i>. Vol 2. MXBS. Cham: Springer International Publishing; 2019:675-691. doi:<a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">10.1007/978-3-030-04161-8_54</a>"},"abstract":[{"lang":"eng","text":"These lecture notes are based on Yang’s talk at the MATRIX program Geometric R-Matrices: from Geometry to Probability, at the University of Melbourne, Dec. 18–22, 2017, and Zhao’s talk at Perimeter Institute for Theoretical Physics in January 2018. We give an introductory survey of the results in Yang and Zhao (Quiver varieties and elliptic quantum groups, 2017. arxiv1708.01418). We discuss a sheafified elliptic quantum group associated to any symmetric Kac-Moody Lie algebra. The sheafification is obtained by applying the equivariant elliptic cohomological theory to the moduli space of representations of a preprojective algebra. By construction, the elliptic quantum group naturally acts on the equivariant elliptic cohomology of Nakajima quiver varieties. As an application, we obtain a relation between the sheafified elliptic quantum group and the global affine Grassmannian over an elliptic curve."}],"OA_place":"repository","title":"How to Sheafify an Elliptic Quantum Group","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1803.06627"}],"alternative_title":["MATRIX Book Series"],"day":"25","oa":1,"article_processing_charge":"No","external_id":{"arxiv":["1803.06627"]},"oa_version":"Preprint","page":"675-691","date_updated":"2025-09-23T11:59:52Z","date_published":"2019-03-25T00:00:00Z","publication":"2017 MATRIX Annals","year":"2019","publisher":"Springer International Publishing","series_title":"MXBS","publication_identifier":{"isbn":["9783030041601"],"eisbn":["9783030041618"],"issn":["2523-3041"],"eissn":["2523-305X"]},"place":"Cham","month":"03"}