# Irreducible representations of E theory

## TL;DR

This paper constructs and analyzes the irreducible representations of E theory related to eleven-dimensional supergravity, revealing their structure, symmetries, and implications for extended spacetime coordinates.

## Contribution

It introduces the E theory analogue of particle representations, showing their connection to supergravity and clarifying the role of E11 symmetries in light cone formalism.

## Key findings

- One irreducible representation matches eleven-dimensional supergravity degrees of freedom.
- E theory duality relations simplify in light cone formalism.
- E11 symmetries underlie recent mysterious symmetries in supergravity.

## Abstract

We construct the E theory analogue of the particles that transform under the Poincare group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of E11 with its vector representation. We show that one such irreducible representation has only the degrees of freedom of eleven dimensional supergravity. This representation is most easily discussed in the light cone formalism and we show that the duality relations found in E theory take a particularly simple form in this formalism. We explain that the mysterious symmetries found recently in the light cone formulation of maximal supergravity theories are part of E11. We also argue that our familiar spacetimes have to be extended by additional coordinates when considering extended objects such as branes.