Nilpotent quiver varieties with multiplicities and symmetrisable crystals

We construct analogues of Nakajima's nilpotent quiver varieties for quivers with multiplicities, by developing new stability conditions for framed nilpotent quiver representations with multiplicities and exploiting their interplay with Hecke correspondences.

Using these new quiver varieties, we extend Saito's geometric construction of Kashiwara crystals of irreducible highest-weight representations of Kac--Moody algebras from the symmetric to the symmetrisable case.