Peter Cameron (School of Mathematical Sciences, Queen Mary, University of London, UK)
13/04/2012 Sextafeira, 13 de Abril de 2012, 14:3015:30, Sala B301
Institute for Interdisciplinary Research  University of Lisbon
Talk 2: Between primitive and 2transitive, II: association schemes and coherent configurations
Coherent configurations were introduced by Donald Higman (and the equivalent
cellular algebras by Weisfeiler and Leman) as a combinatorial and
representationtheoretic tool for the study of permutation groups. However,
a special case, association schemes, had arisen much earlier in statistics
by Bose and several collaborators, and had been generalised in various ways,
notably by Delsarte for applications to coding theory. Every group which is not $2$transitive acts on a nontrivial coherent configuration. But the same is not true for association schemes. A permutation group is called \emph{ASfree} if it preserves no nontrivial association scheme. Such groups must be primitive, but not too many examples are known. I will discuss the existence or nonexistence of ASfree groups in the various O'NanScott classes, and also some generalisations.
http://caul.cii.fc.ul.pt/slides/PeterCameron_talk2.pdf/ 
