The F-valued points of the algebra of strongly regular functions of a Kac-Moody group

Details The F-valued points of the algebra of strongly regular functions of a Kac-Moody group The F-valued points of the algebra of strongly regular functions of a Kac-Moody group

2002-05-07

arxiv.org/abs/math/0205067v1

Mathematics

Algebraic Geometry

41 pages

Scientific paper

The algebra of strongly regular functions F[G_m] on a symmetrizable minimal Kac-Moody group G_m 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 (G_f) x (G_f) of two formal Kac-Moody groups G_f acts on the F-valued points by morphisms. We describe the partition in (G_f) x (G_f)-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 (B_f) x (B_f)-orbits, B_f the standard formal Borel subgroup of G_f.

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