Descent representations and multivariate statistics

Ron M. Adin, Francesco Brenti, Yuval Roichman

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)3051-3082
Number of pages32
JournalTransactions of the American Mathematical Society
Volume357
Issue number8
DOIs
StatePublished - Aug 2005

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