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Hecke Algebras, Difference Operators, and Quasi-Symmetric Functions

✍ Scribed by Florent Hivert

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
470 KB
Volume
155
Category
Article
ISSN
0001-8708

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✦ Synopsis

We define a new action of the symmetric group and its Hecke algebra on polynomial rings whose invariants are exactly the quasi-symmetric polynomials. We interpret this construction in terms of a Demazure character formula for the irreducible polynomial modules of a degenerate quantum group. We use the action of the generic Hecke algebras to define quasi-symmetric and noncommutative analogues of Hall Littlewood functions. We show that these generalized functions share many combinatorial properties with the classical ones.

Nous introduisons de nouvelles actions du groupe syme trique et de son algeÁ bre de Hecke sur les polyno^mes, pour lesquelles les invariants sont les polyno^mes quasisyme triques. Nous interpre tons cette construction en termes de caracteÁ res de Demazure d'un groupe quantique de ge ne re . Nous utilisons l'action de l'algeÁ bre de Hecke ge ne rique pour de finir des analogues quasi-syme triques et non commutatifs des fonctions de Hall Littlewood. Nous montrons que ces fonctions ge ne ralise es ont un certain nombre de proprie teÁ s communes avec les fonctions classiques.

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