Finite dimensional modules over quantum toroidal algebras

Abstract

For all generic q ∈ ℂ*, when $$\\mathfrak{g}$$ g is not of type A 1 , we prove that the quantum toroidal algebra $$U_q(\\mathfrak{g}_{\\rm{tor}})$$ U q ( g t o r ) has no nontrivial finite dimensional simple module.