Spherical buildings and the character of the Steinberg representation

DOI10.1007/BF01390251zbMath0435.20024MaRDI QIDQ1140161

Jacques Tits, Charles W. Curtis, Gustav Isaac Lehrer

Publication date: 1980

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142720

zbMATH Keywords

spherical buildingconnected reductive algebraic groupcharacter of the Steinberg representation

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05)

Related Items

Representations of finite groups, Representation theory and sheaves on the Bruhat-Tits building, Edifices: building-like spaces associated to linear algebraic groups, The Steinberg function of a finite Lie algebra, Cohomology and geometry of Deligne-Lusztig varieties for \(\mathrm{GL}_n\), The space of invariant functions on a finite Lie algebra, Coarse equivalences of Euclidean buildings. (With an appendix by Jeroen Schillewaert and Koen Struyve.), Reflection compound representations of groups of type A//n,B//n or \(C_ n\)., Remarques sur la dualité de Curtis, A New Proof of a Theorem of Solomon-Tits, The cohomology of period domains for reductive groups over finite fields, \(p\)-adic étale cohomology of period domains, The fundamental group of period domains over finite fields, On a formula of Solomon, The Steinberg representation, Involutions, classical groups, and buildings, Branching laws for the Steinberg representation: the rank 1 case, Equivariant Euler characteristics of unitary buildings, The cohomology of \(p\)-adic symmetric spaces, Unnamed Item, The spherical building and regular semisimple elements, Arakelov intersection indices of linear cycles and the geometry of buildings and symmetric spaces., The cohomology of period domains for reductive groups over local fields, Homology groups of Steiner systems, Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings, The split building of a reductive group

Cites Work

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• Groupes reductifs
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• Reductive groups over a local field
• p-adic curvature and the cohomology of discrete subgroups of p-adic groups
• Endomorphisms of linear algebraic groups
• On the Steinberg Character of a Finite Simple Group of Lie Type