Skip to Main content Skip to Navigation
Theses

formules de caracteres pour des representations irreductibles des groupes classiques en egale caracteristique

Abstract : Let p be a prime and G a classical group of type B, C or D defined over an algebraic closure K of the finite field with p elements (if the type of G is B or D, p is odd). Using dual pairs and tilting modules, one can find the character of some irreducible rational representations of G over K. One first obtains character formulas expressed with semi-standard tableaux, outside the validity domain of the Lusztig conjecture. Then one determines the dimension and/or character of the irreducible representations whose highest weight is a fundamental weight, or the sum of two fundamental weights, according to G. In particular, for a given p, one deduces the asymptotic behavior of their dimension when the rank of the group is growing towards infinity. Finally, one gets the simple Weyl modules whose highest weight is a fundamental weight when G is a symplectic group, or a sum of a fundamental weight and of the highest weight of the spin representation when G is a spin group.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00006408
Contributor : Sebastien Foulle <>
Submitted on : Wednesday, July 7, 2004 - 5:20:57 PM
Last modification on : Tuesday, November 19, 2019 - 2:37:20 AM
Long-term archiving on: : Wednesday, September 12, 2012 - 4:35:24 PM

Identifiers

  • HAL Id : tel-00006408, version 1

Collections

Citation

Sebastien Foulle. formules de caracteres pour des representations irreductibles des groupes classiques en egale caracteristique. Mathématiques [math]. Université Claude Bernard - Lyon I, 2004. Français. ⟨tel-00006408⟩

Share

Metrics

Record views

263

Files downloads

2015