Full automorphism groups of association schemes based on isotropic subspaces

TL;DR

This paper determines the full automorphism group of association schemes derived from isotropic subspaces in finite classical polar spaces, extending understanding of symmetries in these combinatorial structures.

Contribution

It provides the first complete characterization of automorphism groups for schemes based on isotropic subspaces in finite polar spaces.

Findings

Automorphism group of the scheme is explicitly determined.

Results unify and extend previous symmetry analyses in polar space schemes.

The work applies to schemes of various dimensions, including extremal cases.

Abstract

The set of all subspaces of a given dimension in a finite classical polar space has a structure of a symmetric association scheme. If the dimension is zero, this is the scheme of the collinearity graph of the space; If the dimension is maximum, it is the dual polar scheme. In this note, we determine the full automorphism group of this scheme.