On generalized hyperpolygons


Schaposnik, L. (2021). On generalized hyperpolygons. Perimeter Institute. https://pirsa.org/21020032


Schaposnik, Laura. On generalized hyperpolygons. Perimeter Institute, Feb. 23, 2021, https://pirsa.org/21020032


          @misc{ pirsa_PIRSA:21020032,
            doi = {10.48660/21020032},
            url = {https://pirsa.org/21020032},
            author = {Schaposnik, Laura},
            keywords = {Mathematical physics},
            language = {en},
            title = {On generalized hyperpolygons},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {feb},
            note = {PIRSA:21020032 see, \url{https://pirsa.org}}

Laura Schaposnik University of Illinois at Chicago


In this talk we will introduce generalized hyperpolygons, which arise as Nakajima-type representations of a comet-shaped quiver, following recent work joint with Steven Rayan. After showing how to identify these representations with pairs of polygons, we shall associate to the data an explicit meromorphic Higgs bundle on a genus-g Riemann surface, where g is the number of loops in the comet. We shall see that, under certain assumptions on flag types, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system.