Kac-Moody groups, hovels and Littelmann paths
We give the definition of a kind of building for a symmetrizable Kac-Moody group over a field endowed with a discrete valuation and with a residue field containing . Due to the lack of some important property of buildings, we call it a hovel. Nevertheless, some good ones remain, for example, the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semisimple case by S. Gaussent and P. Littelmann. In particular, if , the geodesic segments...