Descent Representations and Multivariate Statistics

Details Descent Representations and Multivariate Statistics Descent Representations and Multivariate Statistics

2001-12-07

arxiv.org/abs/math/0112073v2

Mathematics

Combinatorics

46 pages; to appear in Trans. Amer. Math. Soc

Scientific paper

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.

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