# On K(E_9)

@article{Nicolai2004OnK, title={On K(E\_9)}, author={Hermann Nicolai and H. Samtleben}, journal={arXiv: High Energy Physics - Theory}, year={2004} }

We study the maximal compact subgroup K(E_9) of the affine Lie group E_9(9) and its on-shell realization as an R symmetry of maximal N=16 supergravity in two dimensions. We first give a rigorous definition of the group K(E_9), which lives on the double cover of the spectral parameter plane, and show that the infinitesimal action of K(E_9) on the chiral components of the bosons and the fermions is determined in terms of an expansion of the Lie algebra of K(E_9) about the two branch points of…

## 11 Citations

### Infinite-Dimensional Gauge Structure of d=2 N=16 Supergravity

- Mathematics, Physics
- 2006

Dimensional reduction of maximal supergravity to two dimensions leads to an infinite-dimensional (non-local) symmetry group W x E_9 which has a simpler action when the bosonic fields are dualised to…

### Invariance of 11-Dimensional Supergravity

- Physics
- 2005

The hyperbolic Kac-Moody algebra E10 has repeatedly been suggested to play a crucial role in the symmetry structure of M -theory. Recently, following the analysis of the asymptotic behaviour of the…

### Extended E8 invariance of 11-dimensional supergravity

- Physics
- 2006

The hyperbolic Kac-Moody algebra E10 has repeatedly been suggested to play a crucial role in the symmetry structure of M-theory. Recently, following the analysis of the asymptotic behaviour of the…

### Canonical structure of the E10 model and supersymmetry

- Mathematics
- 2015

A coset model based on the hyperbolic Kac–Moody algebra E10 has been conjectured to underly eleven-dimensional supergravity and M theory. In this note we study the canonical structure of the bosonic…

### Gradient representations and affine structures in AEn

- Mathematics
- 2005

We study the indefinite Kac–Moody algebras AEn, arising in the reduction of Einstein's theory from (n + 1) spacetime dimensions to one (time) dimension, and their distinguished maximal regular…

### Hidden symmetries and Dirac fermions

- Physics
- 2005

In this paper, two things are done. First, we analyse the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories…

### Kac-Moody algebras in M-theory

- Mathematics
- 2006

In this thesis, we consider several aspects of over-extended and very-extended Kac-Moody algebras in relation with theories of gravity coupled to matter. In the first part, we focus on the occurrence…

### On Spinorial Representations of Involutory Subalgebras of Kac–Moody Algebras

- MathematicsPartition Functions and Automorphic Forms
- 2020

The representation theory of involutory (or ‘maximal compact’) subalgebras of infinite-dimensional Kac–Moody algebras is largely terra incognita, especially with regard to fermionic (double-valued)…

### Representations of Quantum Minimal Surface Algebrasvia Kac-Moody-theory

- Mathematics
- 2021

We consider epimorphisms from quantum minimal surface algebras onto involutroy subalgebras of split real simply-laced Kac-Moody algebras and provide examples of affine and finite type. We also…

### Representations of Involutory Subalgebras of Affine Kac–Moody Algebras

- MathematicsCommunications in Mathematical Physics
- 2022

We consider the subalgebras of split real, non-twisted affine Kac–Moody Lie algebras that are fixed by the Cartan–Chevalley involution. These infinite-dimensional Lie algebras are not of Kac–Moody…

## References

SHOWING 1-10 OF 30 REFERENCES

### Integrability and canonical structure of d = 2, N = 16 supergravity

- Physics, Mathematics
- 1998

### The topology of U-duality (sub)groups

- Mathematics
- 2004

We discuss the topology of the symmetry groups appearing in compactified (super)gravity, and discuss two applications. First, we demonstrate that for three-dimensional sigma models on a symmetric…

### Time-like T-duality algebra

- Mathematics
- 2004

When compactifying M- or type II string-theories on tori of indefinite space-time signature, their low energy theories involve sigma models on En(n)/Hn, where Hn is a not necessarily compact subgroup…

### On the Geroch Group

- Mathematics
- 1986

2014 The set of stationary, axially symmetric solutions of Einstein’s vacuum field equations is acted on by some infinite dimensional group (Geroch). A precise definition of this group is given as…

### G+++ invariant formulation of gravity and M theories: Exact BPS solutions

- Mathematics
- 2004

We present a tentative formulation of theories of gravity with suitable matter content, including in particular pure gravity in D dimensions, the bosonic efiective actions of M-theory and of the…

### M-theory and E10: Billiards, Branes, and Imaginary Roots

- Mathematics
- 2004

Eleven dimensional supergravity compactified on $T^10$ admits classical solutions describing what is known as billiard cosmology - a dynamics expressible as an abstract (billiard) ball moving in the…

### The structure ofN=16 supergravity in two dimensions

- Physics
- 1989

We extend the previously constructed linear system forN=16 supergravity in two dimensions by including the unphysical gravitino degrees of freedom. This theory has a residualN=16 “superconformal”…