The F-valued points of the algebra of strongly regular functions of a Kac-Moody group
نویسنده
چکیده
Let Gm resp. Gf be the minimal resp. formal Kac-Moody group, associated to a symmetrizable generalized Cartan matrix, over a field F of characteristic 0. Let F [Gm] be the algebra of strongly regular functions on Gm. We denote by Ĝm resp. Ĝf certain monoid completions of Gm resp. Gf , build by using the faces of the Tits cone. We show that there is an action of Ĝf × Ĝf on the spectrum of F-valued points of F [Gm]. As a Ĝf × Ĝf -set it can be identified with a certain quotient of the Ĝf × Ĝf -set Ĝf × Ĝf , build by using Ĝm. We prove a Birkhoff decomposition for the F-valued points of F [Gm]. We describe the stratification of the spectrum of F-valued points of F [Gm] in Gf × Gf -orbits. We show that every orbit can be covered by suitably defined big cells. Mathematics Subject Classification 2000: 17B67, 22E65.
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