A note on the automorphism group of the root lattice of the U-dual modular group

Abstract

We study the inclusion system of the quantum deformed 2 dimensional Yang- Mills root module to the graded root module of the U-dual modular group. The irreducible representation of the U-dual modular group is the quantum deformed black brane throat. We expose the isomorphism between coherent superposition of the topological amplitude and the space of the automorphic forms of the U-dual modular group.