Shifted quiver Yangians and representations from BPS crystals

A bstract We introduce a class of new algebras, the shifted quiver Yangians, as BPS algebras for type IIA string theory on general toric Calabi-Yau three-folds. construct representations Yangian from subcrystals canonical crystal. derive our results via equivariant localization supersymmetric quantum mechanics various framed quivers, where framings are determined by shape subcrystals. Our unify many known state counting problems, including open counting, non-compact D4-branes, and wall crossing phenomena, simply different Yangians. Furthermore, most seem to be new, this suggests existence zoo problems yet studied in detail.