4 papers
Nilpotent quiver varieties with multiplicities and symmetrisable crystals
Victoria Hoskins, Joshua Jackson, Tanguy Vernet
We construct analogues of Nakajima's nilpotent quiver varieties for quivers with multiplicities, by developing new stability conditions for framed nilpotent quiver representations…
Moduli spaces of representations of quivers with multiplicities via non-reductive GIT
Victoria Hoskins, Joshua Jackson, Tanguy Vernet
We construct new moduli spaces of quiver representations with multiplicities, i.e. over rings of truncated power series. This includes moduli of framed representations and analogue…
Counting representations of quivers with multiplicities
Tanguy Vernet
In this thesis, we study counts of quiver representations over finite rings of truncated power series. We prove a plethystic formula relating counts of quiver representations over…
Positivity for toric Kac polynomials in higher depth
Tanguy Vernet
We prove that the polynomials counting locally free, absolutely indecomposable, rank 1 representations of quivers over rings of truncated power series have non-negative coefficient…