Categorization of Heisenberg operators and their infinitely many counterparts in quantum toroidal algebras

A Categorical Quantum Toroidal Action on Hilbert Schemes

We categorify the commutation of nakajima s heisenberg operators and their infinitely many counterparts in the quantum toroidal algebra acting on the grothendieck groups of hilbert schemes.We construct two triple moduli spaces and study their singularity structure from the viewpoint of the minimal model program.We prove that one moduli space is a canonical singularity and the other one is semi-divisorial log terminal.Combining our result with arxiv:1804.03645, one obtains a geometric categorical action on the derived category of hilbert schemes.