On decomposition of modular representations from Cohen-Macaulay geometries

DOI10.1016/0021-8693(90)90197-VzbMath0699.20009MaRDI QIDQ912975

Stephen D. Smith

Publication date: 1990

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

zbMATH Keywords

splittingbuildingsCohen-Macaulay propertyBorel subgroupgroup of Lie typep-local group geometriessporadic \(C_ 3\)-geometry for \(A_ 7\)

Mathematics Subject Classification ID

Geometric group theory (20F65) Modular representations and characters (20C20) Finite simple groups and their classification (20D05) Combinatorial geometries and geometric closure systems (51D20) Other finite nonlinear geometries (51E25) Other finite incidence structures (geometric aspects) (51E30)

Related Items (6)

Weights and covers of chamber systems ⋮ 0-Hecke algebra actions on coinvariants and flags ⋮ On homological properties of locally polar spaces. ⋮ Extensions of cocycles, Cohen-Macaulay geometries, and a vanishing theorem for cohomology of alternating groups. ⋮ (\(q,t\))-analogues and \(GL_{n}({\mathbb{F}}_{q})\) ⋮ On Nonprojective Block Components of Lefschetz Characters for Sporadic Geometries

Cites Work

• Some projective modules determined by sporadic geometries
• Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
• Some exceptional 2-adic buildings
• The modular Hecke algebra and Steinberg representation of finite Chevalley groups (with an appendix by Peter Landrock)
• Minimal parabolic geometries for the sporadic groups
• Universal presheaves on group geometries, and modular representations
• Embeddings of Hecke algebras in group algebras
• The Steinberg component of a finite group with a split (B,N)-pair
• Diagrams for geometries and groups
• Combinatorial methods in the theory of Cohen-Macaulay rings
• Combinatorial decompositions of a class of rings
• Reflection compound representations of groups of type A//n,B//n or \(C_ n\).
• Some aspects of groups acting on finite posets
• Buildings of spherical type and finite BN-pairs
• Cohen-Macaulay quotients of polynomial rings
• A characterization of the modular representations of finite groups with split \((B,N)\)-pairs
• Duality for presheaves on chamber systems, and a related chain complex
• Some sporadic geometries related to PG(3,2)
• A decomposition of the group algebra of a finite Coxeter group
• The spherical building and regular semisimple elements
• Overgroups of Sylow subgroups in sporadic groups
• Computation of 2-modular sheaves and representations forL₄(2)A₇, 3S₆, andM₂₄
• Modular Representations of Finite Groups with Unsaturated Split (B,N)-Pairs
• The Upper Bound Conjecture and Cohen-Macaulay Rings
• On a Theorem of H. Sawada
• Irreducible representations of finite groups of Lie type.
• Modular Representations of Split BN Pairs
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