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

DOI10.1016/j.jalgebra.2017.05.043zbMath1457.20051arXiv1607.00954OpenAlexW2963314396MaRDI QIDQ1682041

Zhenheng Li, Zhuo Li, Claus Mokler

Publication date: 28 November 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.00954

zbMATH Keywords

Kac-Moody groupreductive algebraic monoid\(\mathcal{J}\)-irreducibleinfinite-dimensional algebraic monoidWeyl group orbit

Mathematics Subject Classification ID

Groups with a (BN)-pair; buildings (20E42) Kac-Moody groups (20G44) Algebraic monoids (20M32)

Related Items (1)

Invariant convex subcones of the Tits cone of a linear Coxeter group

Cites Work

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• Faces and maximizer subsets of highest weight modules
• An algebraic geometric model of an action of the face monoid associated to a Kac-Moody group on its building
• Uniqueness and presentation of Kac-Moody groups over fields
• Generic Hecke algebra for Renner monoids.
• Invariant convex subcones of the Tits cone of a linear Coxeter group
• On representations and compactifications of symmetric Riemannian spaces
• Actions of the face monoid associated to a Kac-Moody group on its building
• Analogue of the Bruhat decomposition for algebraic monoids
• The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
• Invariant theory for generalized root systems
• The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids
• Idempotent lattices, Renner monoids and cross section lattices of the special orthogonal algebraic monoids.
• Affine Weyl groups and \(\mathcal J\)-irreducible monoids of adjoint type.
• Linear algebraic monoids.
• The \(\mathbb{F}\)-valued points of the algebra of strongly regular functions of a Kac-Moody group
• Types of reductive monoids
• The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids. II
• Kac-Moody groups, their flag varieties and representation theory
• The cross section lattices and Renner monoids of the odd special orthogonal algebraic monoids
• Extending the Bruhat order and the length function from the Weyl group to the Weyl monoid.
• Groupes reductifs
• NONORTHOGONAL GEOMETRIC REALIZATIONS OF COXETER GROUPS
• THE RENNER MONOIDS AND CELL DECOMPOSITIONS OF THE SYMPLECTIC ALGEBRAIC MONOIDS
• ON CERTAIN COMMUTATIVE SUBALGEBRAS OF A UNIVERSAL ENVELOPING ALGEBRA
• Buildings
• REPRESENTATIONS OF THE RENNER MONOID
• An analogue of a reductive algebraic monoid whose unit group is a Kac-Moody group
• Infinite flag varieties and conjugacy theorems
• Equivalent Subgradient Versions of Hamiltonian and Euler–Lagrange Equations in Variational Analysis
• The Maximal Chains of the Extended Bruhat Orders on the  × -Orbits of an Infinite Renner Monoid

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