Association Scheme on Triples from the Unitary Group

TL;DR

This paper explores association schemes on triples derived from the finite unitary groups acting on isotropic lines, providing a detailed description of their relations and intersection numbers.

Contribution

It introduces a new class of association schemes on triples from the finite unitary groups, expanding the understanding of algebraic combinatorics related to group actions.

Findings

Describes relations and intersection numbers of ASTs from finite unitary groups

Connects group actions with association schemes on triples

Provides foundational structure for further algebraic combinatorics research

Abstract

An association scheme on triples (AST) is a three-dimensional analogue of a classical association scheme. Similar to how a transitive group action produces a Schurian classical association scheme, a two-transitive group action produces an AST. This paper describes the relations and intersection numbers of ASTs from the finite unitary groups acting on the respective isotropic lines.