Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations

Arturo Pianzola, Jun Morita, Taiki Shibata

We provide explicit generators and relations for the affine
Kac-Moody groups, as well as a realization of them as (twisted) loop
groups by means of Galois descent considerations. As a consequence, we
show that the affine Kac-Moody group of type X(r)
N is isomorphic to the
fixed-point subgroup of the affine Kac-Moody group of type X(1)
N under
an action of the Galois group.

Mathematical Journal of Okayama University

65

35

81

0030-1566