A decomposition of Solomon's descent algebra

@article{Garsia1989ADO,
  title={A decomposition of Solomon's descent algebra},
  author={Adriano M. Garsia and Christophe Reutenauer},
  journal={Advances in Mathematics},
  year={1989},
  volume={77},
  pages={189-262}
}
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137 Citations
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137 Citations

Cyclic Descents and P-Partitions
Louis Solomon showed that the group algebra of the symmetric group $$\mathfrak{S}_{n}$$n has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In…
The module structure of the Solomon–Tits algebra of the symmetric group
Nonassociative Solomon's descent algebras
Descent algebras of graded bialgebras were introduced by F. Patras as a generalization of Solomon's descent algebras for Coxeter groups of type $A$, i.e. symmetric groups. The universal enveloping…
A decomposition of the group algebra of a hyperoctahedral group
The descent algebra of a finite Coxeter group W is a subalgebra of the group algebra defined by Solomon. Descent algebras of symmetric groups have properties that are not shared by other Coxeter…
A decomposition of the group algebraof a hyperoctahedral group
The descent algebra of a finite Coxeter group W is a subalgebra of the group algebra defined by Solomon. Descent algebras of symmetric groups have properties that are not shared by other Coxeter…
A Decomposition of the Descent Algebra of a Finite Coxeter Group
The purpose of this paper is twofold. First we aim to unify previous work by the first two authors, A. Garsia, and C. Reutenauer (see [2], [3], [4], [5] and [10]) on the structure of the descent…
A symmetry of the descent algebra of a finite Coxeter group
Homomorphisms between Solomon's descent algebras
Lie idempotent algebras
Cyclotomic Solomon Algebras
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