Descent Representations and Multivariate Statistics

  title={Descent Representations and Multivariate Statistics},
  author={Ron M. Adin and Francesco Brenti and Yuval Roichman},
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… CONTINUE READING
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