The string little algebra

TL;DR

This paper explores the algebraic structure underlying string charges, revealing that the string little algebra is the Borel subalgebra of E9, and connects known string states to this algebraic framework.

Contribution

It identifies the string little algebra as the Borel subalgebra of E9 and links string physical states to this algebraic structure, offering new insights into string symmetries.

Findings

The string little algebra is the Borel subalgebra of E9.

String physical states carry representations of parts of this algebra.

The algebraic framework unifies string charges and states.

Abstract

We consider the string, like point particles and branes, to be an irreducible representation of the semi-direct product of the Cartan involution invariant subalgebra of E11 and its vector representation. We show that the subalgebra that preserves the string charges, the string little algebra, is essentially the Borel subalgebra of E9. We also show that the known string physical states carry a representation of parts of this algebra.