Full automorphism groups of association schemes based on attenuated spaces

TL;DR

This paper determines the full automorphism group of a symmetric association scheme based on attenuated spaces, which generalizes Grassmann and bilinear forms schemes, expanding understanding of their symmetries.

Contribution

It provides the first complete characterization of the automorphism group for association schemes derived from attenuated spaces, extending previous intersection number results.

Findings

Full automorphism group explicitly determined

Automorphism group generalizes known schemes

Enhances understanding of symmetries in association schemes

Abstract

The set of subspaces with a given dimension in an attenuated space has a structure of a symmetric association scheme, which is a generalization of both Grassmann schemes and bilinear forms schemes. In [K. Wang, J. Guo, F. Li, Association schemes based on attenuated space, European J. Combin. 31 (2010) 297--305], its intersection numbers were computed. In this paper, we determine its full automorphism group.