Infinite-dimensional reductive monoids associated to highest weight representations of Kac-Moody groups

2015/11/24 by Zhenheng Li, Zhuo Li, Li, Zhenheng +3
Mathematics · #20E42 #20G44 #20M32 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1511.07697

openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Starting with a highest weight representation of a Kac-Moody group over the complex numbers, we construct a monoid whose unit group is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We show that this monoid has similar properties to those of a J-irreducible reductive linear algebraic monoid. In particular, the monoid is unit regular and has a Bruhat decomposition, and the idempotent lattice of the generalized Renner monoid of the Bruhat decomposition is isomorphic to the face lattice of the convex hull of the Weyl group orbit of the highest weight.

Citations

• Cross-section Lattices of \mathcal J-irreducible Monoids and Orbit Structures of Weight Polytopes

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