English

How to sheafify an elliptic quantum group

Representation Theory 2018-03-20 v1

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.

Keywords

Cite

@article{arxiv.1803.06627,
  title  = {How to sheafify an elliptic quantum group},
  author = {Yaping Yang and Gufang Zhao},
  journal= {arXiv preprint arXiv:1803.06627},
  year   = {2018}
}

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

R2 v1 2026-06-23T00:56:37.473Z