A decomposition of Solomon's descent algebra
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Publication:752844
DOI10.1016/0001-8708(89)90020-0zbMath0716.20006OpenAlexW1969587455MaRDI QIDQ752844
Christophe Reutenauer, Adriano M. Garsia
Publication date: 1989
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0001-8708(89)90020-0
partitionspermutationsfree Lie algebragroup algebrasymmetric groupindecomposable representationsnilpotentsdescent setorthogonal idempotentsdescent classLie monomialsSolomon's descent algebra
Permutations, words, matrices (05A05) Representations of finite symmetric groups (20C30) Identities, free Lie (super)algebras (17B01) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Symmetric groups (20B30) Associated Lie structures for groups (20F40)
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Cites Work
- The Orlik-Solomon algebra on the partition lattice and the free Lie algebra
- On the action of the symmetric group on the free Lie algebra and the partition lattice
- Shuffles of permutations and the Kronecker product
- On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes
- Combinatorics and topology of complements of hyperplanes
- A hyperoctahedral analogue of the free Lie algebra
- Homomorphisms between Solomon's descent algebras
- A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
- Lyndon Words, Free Algebras and Shuffles
- On the Poincaré-Birkhoff-Witt theorem
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