Hecke algebras, difference operators, and quasi-symmetric functions
type: Item
instance of: scholarly article
title: Hecke algebras, difference operators, and quasi-symmetric functions
zbMATH Open document ID: 0990.05129
author: Florent Hivert
published in: Advances in Mathematics
publication date: 2002-08-07T00:00:00Z
review text: Quasi-symmetric functions and noncommutative symmetric functions are two recent generalizations of symmetric functions. The paper under review extends both of these concepts to Hall-Littlewood functions, defining quasi-symmetric Hall-Littlewood functions and noncommutative Hall-Littlewood functions. The development of these two functions parallels that of the ordinary Hall-Littlewood functions: the author first considers that Hall-Littlewood functions can be built up using Hecke algebras and Demazure's character formula [see \textit{G. Duchamp, D. Krob, A. Lascoux, B. Leclerc, T. Scharf} and \textit{J.-Y. Thibon}, Euler-Poincaré characteristic and polynomial representations of Iwashori-Hecke algebras, Publ. Res. Inst. Math. Sci. 31, No. 2, 179-201 (1995; Zbl 0835.05085)], and then extends these techniques to produce quasi-symmetric Hall-Littlewood functions. The author finally employs duality to derive the noncommutative Hall-Littlewood functions.
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 33D80
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1545240
zbMATH Keywords: quasi-symmetric functions
zbMATH Keywords: noncommutative symmetric functions
zbMATH Keywords: Hall-Littlewood functions
reviewed by: Angèle. M. Hamel
describes a project that uses: NCSF
MaRDI profile type: Publication
full work available at URL: aima.1999.1901
OpenAlex ID: W2074762481
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DOI: 10.1006/AIMA.1999.1901
description: scientific article; zbMATH DE number 1545240