## Abstract

Combinatorial identities on Weyl groups of types and are derived from special bases of the corresponding coinvariant algebras. Using the Garsia-Stanton descent basis of the coinvariant algebra of type we give a new construction of the Solomon descent representations. An extension of the descent basis to type , using new multivariate statistics on the group, yields a refinement of the descent representations. These constructions are then applied to refine well-known decomposition rules of the coinvariant algebra and to generalize various identities.

Original language | American English |
---|---|

Title of host publication | Conference in Formal Power Series and Algebraic Combinatorics |

Editors | R. Brak, O. Foda, C. Greenhill, T. Gutman, A. Owczarek |

State | Published - 2002 |