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

2006/09/26 by Claus Mokler, Mokler, Claus
Mathematics · Physics and Astronomy · #20E42 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.GR #math.RT #msc:20E42

paper · pdf · doi:10.48550/arxiv.math/0609726

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

openalex publication_date 2006/09/26 · arxiv created 2009/02/10 · arxiv updated 2009/12/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

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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