Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables

By Nantel Bergeron, Christophe Reutenauer, Mercedes H. Rosas, Mike Zabrocki. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2005

58 citations recorded by the source corpus.

Abstract We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions. The bases for this algebra are indexed by set partitions. We show that there exists a natural inclusion of the Hopf algebra of noncommutative symmetric functions in this larger space. We also consider this algebra as a subspace of noncommutative polynomials and use it to understand the structure of the spaces of harmonics and coinvariants with respect to this collection of noncommutative polynomials and conclude two analogues of Chevalley’s theorem in the noncommutative setting.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4f472073cc6a592f07b76b28db78b4dedc5135da

Citations in the corpus

• THE HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND QUASI-SYMMETRIC FUNCTIONS IN NON-COMMUTATIVE VARIABLES ARE FREE AND CO-FREE (2005, unknown): “This appendix includes the Hasse diagrams for the set compositions of size 3 and 4.”