Descent Representations and Multivariate Statistics

Adin, Ron M.; Brenti, Francesco; Roichman, Yuval

Descent Representations and Multivariate Statistics

Authors

Adin, Ron M.

Brenti, Francesco

Roichman, Yuval

Description

Combinatorial identities on Weyl groups of types $A$ and $B$ are derived from special bases of the corresponding coinvariant algebras. Using the Garsia-Stanton descent basis of the coinvariant algebra of type $A$ we give a new construction of the Solomon descent representations. An extension of the descent basis to type $B$, 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.
46 pages; to appear in Trans. Amer. Math. Soc