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

Claus Mokler
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Abstract

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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Claus Mokler. 2009-02-10. Actions of the face monoid associated to a Kac-Moody group on its building. https://arxiv.org/abs/math/0609726

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