An algebraic geometric model of an action of the face monoid associated to a Kac-Moody group on its building
نویسنده
چکیده
We described in [M1] a monoid b G, the face monoid, acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group G. We found in [M5] two natural extensions of the action of the Kac-Moody group G on its building Ω to actions of the face monoid b G on the building Ω. Now we give an algebraic geometric model of one of these actions of the face monoid b G on the building Ω, where Ω is obtained as a part of the F-valued points of the spectrum of homogeneous prime ideals of the Cartan algebra of the Kac-Moody group G. We determine all F-valued points of the spectrum of homogeneous prime ideals of the Cartan algebra of G.
منابع مشابه
Actions of the face monoid associated to a Kac-Moody group on its building
We described in [7] a monoid b G acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid with unit group a Kac-Moody group G. Now we find natural extensions of the action of the Kac-Moody group G on its building Ω to actions of the monoid b G on Ω. These extensions are partly motivated by represen...
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