Descent representations and multivariate statistics

R.M. Adin; F. Brenti; Y. Roichman

Descent representations and multivariate statistics

R.M. Adin, F. Brenti, Y. Roichman

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Combinatorial identities on Weyl groups of types and are derived from special bases of the corresponding coinvariant algebras. Using the Garsia-Stanton descent basis of the coinvariant algebra of type we give a new construction of the Solomon descent representations. An extension of the descent basis to type , 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 language	American English
Title of host publication	Conference in Formal Power Series and Algebraic Combinatorics
Editors	R. Brak, O. Foda, C. Greenhill, T. Gutman, A. Owczarek
State	Published - 2002

Bibliographical note

Place of conference:University of Melbourne, Australia

Cite this

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title = "Descent representations and multivariate statistics",

abstract = "Combinatorial identities on Weyl groups of types and are derived from special bases of the corresponding coinvariant algebras. Using the Garsia-Stanton descent basis of the coinvariant algebra of type we give a new construction of the Solomon descent representations. An extension of the descent basis to type , 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.",

author = "R.M. Adin and F. Brenti and Y. Roichman",

note = "Place of conference:University of Melbourne, Australia",

year = "2002",

language = "American English",

editor = "R. Brak and O. Foda and C. Greenhill and T. Gutman and A. Owczarek",

booktitle = "Conference in Formal Power Series and Algebraic Combinatorics",

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T1 - Descent representations and multivariate statistics

AU - Adin, R.M.

AU - Brenti, F.

AU - Roichman, Y.

N1 - Place of conference:University of Melbourne, Australia

PY - 2002

Y1 - 2002

N2 - Combinatorial identities on Weyl groups of types and are derived from special bases of the corresponding coinvariant algebras. Using the Garsia-Stanton descent basis of the coinvariant algebra of type we give a new construction of the Solomon descent representations. An extension of the descent basis to type , 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.

AB - Combinatorial identities on Weyl groups of types and are derived from special bases of the corresponding coinvariant algebras. Using the Garsia-Stanton descent basis of the coinvariant algebra of type we give a new construction of the Solomon descent representations. An extension of the descent basis to type , 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.

UR - http://www.ams.org/journals/tran/2005-357-08/S0002-9947-04-03494-4/

M3 - Conference contribution

BT - Conference in Formal Power Series and Algebraic Combinatorics

A2 - Brak, R.

A2 - Foda, O.

A2 - Greenhill, C.

A2 - Gutman, T.

A2 - Owczarek, A.

ER -

Descent representations and multivariate statistics

Abstract

Bibliographical note

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