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

TL;DR

This paper explores the automorphism group of the root lattice related to the U-dual modular group, revealing connections with quantum deformations and topological amplitudes in string theory.

Contribution

It introduces a novel analysis of the automorphism group of the root lattice in the context of U-dual modular symmetry, linking quantum deformations and topological amplitudes.

Findings

Identifies an isomorphism between topological amplitudes and automorphic forms.

Establishes a connection between quantum deformed black branes and the U-dual modular group.

Provides new insights into the structure of the automorphism group in string theory contexts.

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.