Loop Grassmannians of quivers and affine quantum groups

Abstract: We construct for each choice of a quiver $Q$, a cohomology theory $A$ and a poset $P$ a "loop Grassmannian" $\mathcal{G}<sup>P(Q,A)$. This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms. The addition of a dilation torus $\mathcal{D}\subset\mathbb{G}<em>m<sup>2$ gives a quantization $\mathcal{G}^P</em>\mathcal{D}(Q,A)$. The construction is motivated by the program of introducing an inner cohomology theory in algebraic geometry adequate for the Geometric Langlands program ['Some extensions of the notion of loop Grassmannians', Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardesic issue. No. 532, (2017) 53--74.] and on the construction of affine quantum groups from generalized cohomologies ArXiv: 1708.01418.