Association schemes obtained from the action of the general unitary group on isotropic vectors

TL;DR

This paper explores a new family of association schemes derived from the action of general unitary groups on isotropic vectors in finite unitary spaces, providing parameter calculations and character tables.

Contribution

It introduces an infinite family of association schemes from unitary group actions and fully determines their parameters and character tables.

Findings

Parameters of the association schemes are explicitly computed.

Character tables for all nontrivial schemes are determined.

The schemes exhibit transitive action on isotropic vectors.

Abstract

An infinite family of association schemes obtained from the general unitary groups acting transitively on the sets of isotropic vectors in the finite unitary spaces are investigated. We compute the parameters and determine the character tables for all nontrivial commutative association schemes belonging to this family.