Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation

Quiver Hecke algebras and generalisations of Iwahori-Hecke algebras

Abstract : This thesis is devoted to the study of quiver Hecke algebras and some generalisations of Iwahori-Hecke algebras. We begin with two results concerning quiver Hecke algebras, first when the quiver has several connected components and second when the quiver has an automorphism of finite order. We then recall an isomorphism of Brundan-Kleshchev and Rouquier between Ariki-Koike algebras and certain cyclotomic quiver Hecke algebras. From this, on the one hand we deduce that a well-known important Morita equivalence between Ariki--Koike algebras comes from an isomorphism, on the other hand we give a cyclotomic quiver Hecke-like presentation for the Hecke algebra of type G(r,p,n). We also generalise the isomorphism of Brundan-Kleshchev to prove that cyclotomic Yokonuma-Hecke algebras are particular cases of cyclotomic quiver Hecke algebras. Finally, we study a problem of algebraic combinatorics, related to the representation theory of Ariki-Koike algebras. Using the abacus representation of partitions and solving, via an existence theorem for binary matrices, a constrained optimisation problem with integer variables, we prove that a stuttering multiset of residues necessarily comes from a stuttering multipartition.
Document type :
Complete list of metadata

Cited literature [88 references]  Display  Hide  Download
Contributor : ABES STAR :  Contact
Submitted on : Thursday, December 13, 2018 - 3:44:14 PM
Last modification on : Tuesday, January 4, 2022 - 4:47:00 AM
Long-term archiving on: : Thursday, March 14, 2019 - 3:05:32 PM


Version validated by the jury (STAR)


  • HAL Id : tel-01954325, version 1


Salim Rostam. Quiver Hecke algebras and generalisations of Iwahori-Hecke algebras. Representation Theory [math.RT]. Université Paris-Saclay, 2018. English. ⟨NNT : 2018SACLV063⟩. ⟨tel-01954325⟩



Record views


Files downloads