Actions of the face monoid associated to a Kac-Moody group on its building

Details Actions of the face monoid associated to a Kac-Moody group on its building Actions of the face monoid associated to a Kac-Moody group on its building

2006-09-26

arxiv.org/abs/math/0609726v2

Mathematics

Group Theory

37 pages, a new introduction, new results added, some typos corrected

Scientific paper

We described in [M1] a monoid 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. Now we find natural extensions of the action of the Kac-Moody group on its building to actions of this monoid. These extensions are partly motivated by representation theory and the combinatorics of the faces of the Tits cone.

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