The actions of \(S_{n+1}\) and \(S_ n\) on the cohomology ring of a Coxeter arrangement of type \(A_{n-1}\)

DOI10.1007/BF02567941zbMath0886.57029OpenAlexW2052917454MaRDI QIDQ1352970

Giovanni Gaiffi

Publication date: 22 April 1998

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156216

zbMATH Keywords

symmetric groupCoxeter arrangementcohomology ring\(S_ n\)-module

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Representations of finite symmetric groups (20C30) Finite transformation groups (57S17)

Related Items

Equivariant cohomology of the moduli space of genus three curves with symplectic level two structure via point counts ⋮ A type \(B\) analog of the Whitehouse representation ⋮ The Cohomology of $$\mathcal{M}_{0,n}$$ as an FI-Module ⋮ Polynomial splitting measures and cohomology of the pure braid group ⋮ Cohomology of the toric arrangement associated with \(A_n\) ⋮ Trimming the permutahedron to extend the parking space ⋮ Equivariant cohomology of moduli spaces of genus three curves with level two structure ⋮ Symmetric group actions on the cohomology of configurations in \(\mathbb R^d\). ⋮ Internal zonotopal algebras and the monomial reflection groups \(G(m,1,n)\) ⋮ Unnamed Item ⋮ Representation stability for the pure cactus group ⋮ Correction to: ``Cohomology of the toric arrangement associated with \(A_n\)

Cites Work

• Unnamed Item
• On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes
• Combinatorics and topology of complements of hyperplanes
• Hidden \(\Sigma_{n+1}\)-actions
• The tree representation of \(\Sigma_{n+1}\)
• On the Poincaré Series Associated with Coxeter Group Actions on Complements of Hyperplanes
• A toral configuration space and regular semisimple conjugacy classes