Algebraic Aspects of Matrix Theory on T^d

TL;DR

This paper explores the algebraic structure of U duality groups in M-theory compactified on tori, revealing how p-branes and other states form representations of these groups using Matrix theory.

Contribution

It demonstrates the $E_d$ structure and how various states in M-theory form representations of the U duality group, providing new insights into the algebraic aspects of matrix theory.

Findings

Identification of the $E_d$ duality group structure.

Representation of p-branes within the U duality group.

Inclusion of additional states forming group representations.

Abstract

We study the exceptional U duality group $E_d$ of M-theory compactified on a d-torus and its representations using Matrix theory. We exhibit the $E_d$ structure and show that p-branes wrapped or unwrapped around the longitudinal direction form representations of the U duality group together with other, more mysterious, states.