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Mathematics > Representation Theory

Title: How to sheafify an elliptic quantum group

Abstract: We give an introductory survey of the results in arXiv: 1708.01418. 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.
Comments: 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. 12 pages, expository paper, submitted to the MATRIX Annals
Subjects: Representation Theory (math.RT)
Cite as: arXiv:1803.06627 [math.RT]
  (or arXiv:1803.06627v1 [math.RT] for this version)

Submission history

From: Gufang Zhao [view email]
[v1] Sun, 18 Mar 2018 09:06:33 GMT (134kb,D)