Spin covers of maximal compact subgroups of Kac-Moody groups and spin-extended Weyl groups

DOI10.1515/jgth-2016-0034zbMath1390.20048arXiv1502.07294OpenAlexW2963237646MaRDI QIDQ524629

Sebastian Weiß, David Ghatei, Max Horn, Ralf Köhl (né Gramlich)

Publication date: 3 May 2017

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.07294

zbMATH Keywords

Cartan matrixWeyl groupClifford algebraDynkin diagrambuildingKac-Moody groupamalgam groupCartan-Chevalley involutiongeneralised spin representationspin coveruniversal enveloping group

Mathematics Subject Classification ID

Buildings and the geometry of diagrams (51E24) Hyperbolic groups and nonpositively curved groups (20F67) Groups with a (BN)-pair; buildings (20E42) Kac-Moody groups (20G44)

Related Items (5)

On spinorial representations of involutory subalgebras of Kac-Moody algebras ⋮ Representations of involutory subalgebras of affine Kac-Moody algebras ⋮ Fundamental groups of split real Kac-Moody groups and generalized real flag manifolds ⋮ Extending generalized spin representations ⋮ Orthogonal forms of Kac-Moody groups are acylindrically hyperbolic.

Cites Work

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• Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
• Uniqueness and presentation of Kac-Moody groups over fields
• Final group topologies, Kac-Moody groups and Pontryagin duality
• Generators and relations in compact Lie groups
• Building buildings
• Buildings of spherical type and finite BN-pairs
• Twin trees. I
• Compact projective planes. With an introduction to octonion geometry
• Open subgroups of locally compact Kac-Moody groups.
• On topological twin buildings and topological split Kac-Moody groups
• Normalisateurs de tores. I: Groupes de Coxeter etendus
• Acylindrically hyperbolic groups
• Diagram Geometry
• Iwasawa decompositions of split Kac-Moody groups
• Clifford Algebras and Lie Theory
• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Defining amalgams of compact Lie groups
• The Subgroups of a Free Product of Two Groups with an Amalgamated Subgroup
• Automorphisms of trivalent graphs
• The structure of compact groups. A primer for the student -- a handbook for the expert
• Epimorphisms of generalized polygons. I: Geometrical characterizations
• Orthogonal forms of Kac-Moody groups are acylindrically hyperbolic.

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