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Around Solomon’s Descent Algebras

✍ Scribed by C. Bonnafé; G. Pfeiffer

Publisher
Springer Netherlands
Year
2008
Tongue
English
Weight
647 KB
Volume
11
Category
Article
ISSN
1386-923X

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📜 SIMILAR VOLUMES

Homomorphisms between Solomon's descent
Homomorphisms between Solomon's descent algebras
✍ F. Bergeron; A. Garsia; C. Reutenauer 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 582 KB

In a previous paper (see A. Garsia and C. Reutenauer (Adt,. in Math. 77, 1989, 189-262)). we have studied algebraic properties of the descent algebras X,,, and shown how these are related to the canonical decomposition of the free Lie algebra corresponding to a version of the PoincarE-Birkhoff-Witt

A generating set of Solomon's descent al
A generating set of Solomon's descent algebra
✍ Manfred Schocker 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 90 KB

Solomon's descent algebra is generated by sums of descent classes corresponding to certain hook shapes. This particularly implies that the ring of class functions of any finite symmetric group S n is generated by the irreducible characters corresponding to certain hook partitions of n. As another co

Duality between Quasi-Symmetrical Functi
Duality between Quasi-Symmetrical Functions and the Solomon Descent Algebra
✍ C. Malvenuto; C. Reutenauer 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 650 KB

The ring QSym of quasi-symmetric functions is naturally the dual of the Solomon descent algebra. The product and the two coproducts of the first (extending those of the symmetric functions) correspond to a coproduct and two products of the second, which are defined by restriction from the symmetric

Orlik–Solomon Type Algebras
Orlik–Solomon Type Algebras
✍ David Forge; Michel Las Vergnas 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 92 KB

We introduce χ-algebras, and show that a χ-algebra has the NBC basis property. We also show that a certain ideal used in the construction has the so-called BC basis property. The Orlik-Solomon algebra of a matroid, the Orlik-Terao algebra of a set of vectors, and the Cordovil algebra of an oriented