Descent representations and multivariate statistics
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- by Ron M. Adin, Francesco Brenti and Yuval Roichman PDF
- Trans. Amer. Math. Soc. 357 (2005), 3051-3082 Request permission
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.References
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Additional Information
- Ron M. Adin
- Affiliation: Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan 52900, Israel
- Email: radin@math.biu.ac.il
- Francesco Brenti
- Affiliation: Dipartimento di Matematica, Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
- MR Author ID: 215806
- Email: brenti@mat.uniroma2.it
- Yuval Roichman
- Affiliation: Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan 52900, Israel
- Email: yuvalr@math.biu.ac.il
- Received by editor(s): October 13, 2002
- Received by editor(s) in revised form: August 15, 2003
- Published electronically: July 16, 2004
- Additional Notes: The research of all authors was supported in part by the EC’s IHRP programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272, by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities, and by internal research grants from Bar-Ilan University
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 3051-3082
- MSC (2000): Primary 05E10, 13A50; Secondary 05A19, 13F20, 20C30
- DOI: https://doi.org/10.1090/S0002-9947-04-03494-4
- MathSciNet review: 2135735