Loop Grassmannians of Quivers and Affine Quantum Groups
Mirković I, Yang Y, Zhao G. 2022.Loop Grassmannians of Quivers and Affine Quantum Groups. In: Representation Theory and Algebraic Geometry. Trends in Mathematics, , 347–392.
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Author
Mirković, Ivan;
Yang, Yaping;
Zhao, GufangISTA
Book Editor
Baranovskky, Vladimir;
Guay, Nicolas;
Schedler, Travis
Department
Series Title
Trends in Mathematics
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).
Publishing Year
Date Published
2022-06-16
Book Title
Representation Theory and Algebraic Geometry
Publisher
Springer Nature; Birkhäuser
Acknowledgement
I.M. thanks Zhijie Dong for long-term discussions on the material that entered this work. We thank Misha Finkelberg for pointing out errors in earlier versions. His advice and his insistence have led to a much better paper. A part of the writing was done at the conference at IST (Vienna) attended by all coauthors. We therefore thank the organizers of the conference and the support of ERC Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593. The work of I.M. was partially supported by NSF grants. The work of Y.Y. was partially supported by the Australian Research Council (ARC) via the award DE190101231. The work of G.Z. was partially supported by ARC via the award DE190101222.
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347-392
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Cite this
Mirković I, Yang Y, Zhao G. Loop Grassmannians of Quivers and Affine Quantum Groups. In: Baranovskky V, Guay N, Schedler T, eds. Representation Theory and Algebraic Geometry. 1st ed. TM. Cham: Springer Nature; Birkhäuser; 2022:347-392. doi:10.1007/978-3-030-82007-7_8
Mirković, I., Yang, Y., & Zhao, G. (2022). Loop Grassmannians of Quivers and Affine Quantum Groups. In V. Baranovskky, N. Guay, & T. Schedler (Eds.), Representation Theory and Algebraic Geometry (1st ed., pp. 347–392). Cham: Springer Nature; Birkhäuser. https://doi.org/10.1007/978-3-030-82007-7_8
Mirković, Ivan, Yaping Yang, and Gufang Zhao. “Loop Grassmannians of Quivers and Affine Quantum Groups.” In Representation Theory and Algebraic Geometry, edited by Vladimir Baranovskky, Nicolas Guay, and Travis Schedler, 1st ed., 347–92. TM. Cham: Springer Nature; Birkhäuser, 2022. https://doi.org/10.1007/978-3-030-82007-7_8.
I. Mirković, Y. Yang, and G. Zhao, “Loop Grassmannians of Quivers and Affine Quantum Groups,” in Representation Theory and Algebraic Geometry, 1st ed., V. Baranovskky, N. Guay, and T. Schedler, Eds. Cham: Springer Nature; Birkhäuser, 2022, pp. 347–392.
Mirković I, Yang Y, Zhao G. 2022.Loop Grassmannians of Quivers and Affine Quantum Groups. In: Representation Theory and Algebraic Geometry. Trends in Mathematics, , 347–392.
Mirković, Ivan, et al. “Loop Grassmannians of Quivers and Affine Quantum Groups.” Representation Theory and Algebraic Geometry, edited by Vladimir Baranovskky et al., 1st ed., Springer Nature; Birkhäuser, 2022, pp. 347–92, doi:10.1007/978-3-030-82007-7_8.
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