| Abstract: |
I will discuss the computations of elliptic genera/BPS partition functions from the Jeffery-Kirwan residues. For quiver gauge theories satisfying certain conditions, (part of) the information of the counting can be encoded by the crystal melting models, extending the previous cases of the toric ones. We could also recover the standard quiver Yangians/BPS algebras from the JK residue formula and understand to what extent these algebras would apply to arbitrary quivers. This would further allow us to construct a new type of algebra which we call the double quiver Yangians/algebras. The double quiver algebras would work not only for quivers with 4 supercharges (such as those arised from toric Calabi-Yau 3-folds), but also for quivers with 2 supercharges (such as those arised from toric Calabi-Yau 4-folds), where the usual construction of the quiver Yangians would meet problems. I shall also mention the issues when applying this method to the quivers that do not satisfy our conditions. This is based on a joint work with Masahito Yamazaki. |
