Kac--Moody groups and automorphic forms in low dimensional supergravity theories

@article{Bao2016KacMoodyGA,
  title={Kac--Moody groups and automorphic forms in low dimensional supergravity theories},
  author={Ling Bao and Lisa Carbone},
  journal={arXiv: High Energy Physics - Theory},
  year={2016}
}
Kac--Moody groups $G$ over $\mathbb{R}$ have been conjectured to occur as symmetry groups of supergravity theories dimensionally reduced to dimensions less than 3, and their integral forms $G(\mathbb{Z})$ conjecturally encode quantized symmetries. In this review paper, we briefly introduce the conjectural symmetries of Kac--Moody groups in supergravity as well as the known evidence for these conjectures. We describe constructions of Kac--Moody groups over $\R$ and $\Z$ using certain choices of… 

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References

SHOWING 1-10 OF 62 REFERENCES
Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
Kac-Moody groups $G$ over $\mathbb{R}$ have been conjectured to occur as symmetry groups of supergravities in dimensions less than 3, and their integer forms $G(\mathbb{Z})$ are conjecturally
INFINITE DIMENSIONAL CHEVALLEY GROUPS AND KAC-MOODY GROUPS OVER Z
Let A be a symmetrizable generalized Cartan matrix. Let g be the corresponding Kac-Moody algebra. Let G(R) be Tits’ Kac-Moody group functor over commutative rings R associated to g. Then G(R) is
Uniqueness of representation--theoretic hyperbolic Kac--Moody groups over $\Z$
For a simply laced and hyperbolic Kac--Moody group $G=G(R)$ over a commutative ring $R$ with 1, we consider a map from a finite presentation of $G(R)$ obtained by Allcock and Carbone to a
Two conjectures on gauge theories, gravity, and infinite dimensional Kac-Moody groups
We propose that the structure of gauge theories, the (2,0) and little-string theories is encoded in a unique function on the real group manifold E10(R). The function is invariant under the maximal
Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac– Moody groups. In particular, we analyse the
EXISTENCE OF LATTICES IN KAC–MOODY GROUPS OVER FINITE FIELDS
Let be a Kac–Moody Lie algebra. We give an interpretation of Tits' associated group functor using representation theory of and we construct a locally compact "Kac–Moody group" G over a finite field
Higher-order M-theory corrections and the Kac–Moody algebra E10
It has been conjectured that the classical dynamics of M-theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E10/K(E10), where K(E10) is the maximal compact
Eisenstein series for higher-rank groups and string theory amplitudes
Scattering amplitudes of superstring theory are strongly constrained by the requirement that they be invariant under dualities generated by discrete subgroups, E_n(Z), of simply-laced Lie groups in
Eisenstein series for infinite-dimensional U-duality groups
A bstractWe consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these
...
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