The F-valued points of the algebra of strongly regular functions of a Kac-Moody group
Abstract
The algebra of strongly regular functions F[Gm] on a symmetrizable minimal Kac-Moody group Gm over a field F of characteristic zero has been introduced by V. Kac and D. Peterson as a coordinate ring of the minimal Kac-Moody group. We determine its F-valued points. The product (Gf) x (Gf) of two formal Kac-Moody groups Gf acts on the F-valued points by morphisms. We describe the partition in (Gf) x (Gf)-orbits, and the closure relation of the orbits. We give stratified transversal slices to the orbits. We define and describe big cells of each orbit. We describe the partition in (Bf) x (Bf)-orbits, Bf the standard formal Borel subgroup of Gf.
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