Speaker
Description
Delsarte theory has been extended to the study of subsets in an increasing variety of association schemes in recent years, with many different motivations and applications. Tools originally developed for the study of error-correcting codes in the Hamming scheme and combinatorial $t$-designs in the Johnson scheme apply equally well in association schemes with irrational eigenvalues. The goal of the talk is to study the Delsarte $T$-designs in an assocaition scheme with irrational eigenvalues. We show that, for any subset $T$ of eigenspaces, a $T$-design must also be a $T'$-design where $T'$ the closure of $T$ under the action of the Galois group of the splitting field of the association scheme, acting on primitive idempotents. Conjugacy class schemes of finite groups will be the main examples explored. This is based on joint work with Jesse Lansdown (Galway).