A decomposition of the descent algebra of a finite Coxeter group

DOI10.1023/A:1022481230120zbMath0798.20031OpenAlexW1524416588MaRDI QIDQ686008

Publication date: 1 November 1993

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1022481230120

zbMATH Keywords

symmetric groups representations finite Coxeter groups primitive idempotents radical descent algebra hyperoctahedral groups parabolic Burnside algebras

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Frobenius induction, Burnside and representation rings (19A22)

Related Items (45)

The units of a partial Burnside ring relative to the Young subgroups of a symmetric group ⋮ Transformation à la Foata for special kinds of descents and excedances ⋮ Fourier transform over semi-simple algebras and harmonic analysis for probabilistic algorithms ⋮ Hyperoctahedral decomposition of Hochschild homology ⋮ Cohomology of Coxeter arrangements and Solomon’s descent algebra ⋮ Lefschetz invariants and Young characters for representations of the hyperoctahedral groups ⋮ NONORTHOGONAL GEOMETRIC REALIZATIONS OF COXETER GROUPS ⋮ Generalized Burnside algebra of type B_{n} ⋮ Carter-Payne homomorphisms and Jantzen filtrations. ⋮ Eulerian representations for real reflection groups ⋮ Properties of the descent algebras of type $D$. ⋮ The Steinberg torus of a Weyl group as a module over the Coxeter complex ⋮ A type $B$ analog of the Whitehouse representation ⋮ A natural idempotent in the descent algebra of a finite Coxeter group ⋮ The peak algebra of the symmetric group ⋮ Descent algebras, hyperplane arrangements, and shuffling cards ⋮ Spectral properties of descent algebra elements. ⋮ On the quiver presentation of the descent algebra of the symmetric group. ⋮ Semisimple orbits of Lie algebras and card-shuffling measures on Coxeter groups ⋮ Shuffle bialgebras. ⋮ Computations for Coxeter arrangements and Solomon's descent algebra. III: Groups of rank seven and eight. ⋮ An inductive approach to Coxeter arrangements and Solomon's descent algebra. ⋮ Suspension splittings and self-maps of flag manifolds ⋮ Cyclotomic Solomon algebras. ⋮ Representation theory of Mantaci-Reutenauer algebras. ⋮ Orthogonal idempotents in the descent algebra of $B_ n$ and applications ⋮ Symbolic manipulation for the study of the descent algebra of finite Coxeter groups ⋮ On the quiver of the descent algebra. ⋮ A symmetry of the descent algebra of a finite Coxeter group. ⋮ Weak Bruhat order on the set of faces of the permutohedron and the associahedron. ⋮ A Solomon descent theory for the wreath products $G\wr\mathfrak S_n$ ⋮ Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systems ⋮ Descent distribution on Catalan words avoiding a pattern of length at most three ⋮ Coloured peak algebras and Hopf algebras. ⋮ Eulerian representations for real reflection groups ⋮ A quiver presentation for Solomon's descent algebra. ⋮ A multiplication rule for the descent algebra of type $D$ ⋮ Hopf algebra of the planar binary trees ⋮ Around Solomon's descent algebras. ⋮ On Reflection Subgroups of Finite Coxeter Groups ⋮ The excedance set of a permutation ⋮ Counting semisimple orbits of finite Lie algebras by genus ⋮ The table of marks, the Kostka matrix, and the character table of the symmetric group ⋮ Random walks and hyperplane arrangements ⋮ On the quiver presentation of the descent algebra of the hyperoctahedral group.

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