@inbook{12303,
  abstract     = {We construct for each choice of a quiver Q, a cohomology theory A, and a poset P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms. The addition of a “dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated by the program of introducing an inner cohomology theory in algebraic geometry adequate for the Geometric Langlands program (Mirković, Some extensions of the notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic quantum groups, preprint. arxiv1708.01418).},
  author       = {Mirković, Ivan and Yang, Yaping and Zhao, Gufang},
  booktitle    = {Representation Theory and Algebraic Geometry},
  editor       = {Baranovskky, Vladimir and Guay, Nicolas and Schedler, Travis},
  isbn         = {9783030820060},
  issn         = {2297-024X},
  pages        = {347--392},
  publisher    = {Springer Nature; Birkhäuser},
  title        = {{Loop Grassmannians of Quivers and Affine Quantum Groups}},
  doi          = {10.1007/978-3-030-82007-7_8},
  year         = {2022},
}