Representation theory of association schemes

This thesis is motivated by the algebraic treatment given to association schemes and its natural occurrence in the theory of finite permutation groups.The present work deals with the representation theory of association schemes, which is the study of representations of the underlying adjacency algebra of the association scheme. In particular, this work is concerned with association schemes called "group-case" association schemes, arising from the action of a finite group G on G/H, where H is a subgroup of G and where G/H denotes the set of right cosets of H in G. The main purpose of this thesis is to obtain an induction formula for the characters of group-case association schemes. The method used in this regard is the condensation technique introduced by J. A. Green in 1980. This thesis also presents some results and observations on the semisimplicity of adjacency algebras of association schemes.This work also associates a group-case association scheme to an approach to Foulkes' conjecture suggested by Black and List. In this regard a computational study of the problem carried out in the present work answers a question of Black and List to the affirmative in special cases.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2004

Author dc:creator

• Jacob, Juby

Contributors dc:contributor

• Hiß, Gerhard

• info:eu-repo/classification/ddc/510
• Assoziationsschema
• Darstellungstheorie
• Mathematik
• Association Schemes
• Group-case association schemes

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-114236%22

OAI record oai:identifier

https://publications.rwth-aachen.de/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Apublications.rwth-aachen.de%3A51990