%0 Journal Article
%T Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras
%A G. Duchamp
%A F. Hivert
%A J. -Y. Thibon
%J Mathematics
%D 2001
%I arXiv
%X This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young tableaux (free symmetric functions) and packed integer matrices (matrix quasi-symmetric functions). Free quasi-symmetric functions provide a kind of noncommutative Frobenius characteristic for a certain category of modules over the 0-Hecke algebras. New examples of indecomposable $H_n(0)$-modules are discussed, and the homological properties of $H_n(0)$ are computed for small $n$. Finally, the algebra of matrix quasi-symmetric functions is interpreted as a convolution algebra.
%U http://arxiv.org/abs/math/0105065v1