$E_{11}$, SL(32) and Central Charges

TL;DR

This paper explores the structure of the $E_{11}$ algebra, revealing how certain representations correspond to central charges in eleven-dimensional supersymmetry, thus linking algebraic structures to physical symmetries.

Contribution

It demonstrates that specific $A_{10}$ representations within $E_{11}$ correspond to central charges, providing a new algebraic perspective on supersymmetry in M-theory.

Findings

Rank two and five antisymmetric representations are identified with central charges.

$E_{11}$ contains representations corresponding to space-time translations.

SL(32) symmetry plays a key role in understanding these representations.

Abstract

We show that the $E_{11}$ representation that contains the space-time translation generators also contains the rank two and five totally anti-symmetric representations of $A_{10}$. By studying the behaviour of these latter $A_{10}$ representations under SL(32), which we argue is contained in the Cartan involution invariant sub-algebra of $E_{11}$, we find that the rank two and five totally anti-symmetric representations must be identified with the central charges of the eleven dimensional supersymmetry algebra.