Hecke algebras, generalisations and representation theory

Abstract : Iwahori–Hecke algebras associated to Weyl groups appear naturally in the study of finite reductive groups as endomorphism rings of the permutation representation with respect to a Borel subgroup. They can also be defined independently as deformations of group algebras of finite Coxeter groups. The aim of this memoir is to study some aspects of the representation theory of Iwahori–Hecke algebras and the way they generalise in the cases of • cyclotomic Hecke algebras, which are obtained as deformations of group algebras of complex reflection groups, • Ariki–Koike algebras, which are obtained as generalisations of Iwahori–Hecke algebras of types A and B, • Yokonuma–Hecke algebras, which are obtained in the study of finite reductive groups as endomorphism rings of the permutation representation with respect to a maximal unipotent subgroup. In the process, we will also study another family of algebras associated to complex reflection groups, the rational Cherednik algebras, whose representation theory has many connections with the representation theory of Hecke algebras. The aspects of the representation theory of these algebras on which we will focus will be the parametrisation and description of the irreducible representations in the semisimple and non-semisimple case, the block structure, the symmetric algebra structure and the determination of the decomposition matrix with respect to a specialisation.
Document type :
Habilitation à diriger des recherches
Complete list of metadatas

Cited literature [149 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/tel-01411063
Contributor : Maria Chlouveraki <>
Submitted on : Tuesday, December 6, 2016 - 11:22:35 PM
Last modification on : Wednesday, January 23, 2019 - 2:39:26 PM
Long-term archiving on : Tuesday, March 21, 2017 - 6:46:29 AM

File

Identifiers

  • HAL Id : tel-01411063, version 1

Citation

Maria Chlouveraki. Hecke algebras, generalisations and representation theory. Mathematics [math]. Universite de Versailles, 2016. ⟨tel-01411063⟩

Share

Metrics

Record views

339

Files downloads

370