Suborbits of a point stabilizer in the orthogonal group on the last subconstituent of orthogonal dual polar graphs

TL;DR

This paper investigates the structure of suborbits of point stabilizers in orthogonal groups acting on the last subconstituent of orthogonal dual polar graphs over finite fields, providing detailed classifications and related algebraic structures.

Contribution

It determines all suborbits of a point-stabilizer in the orthogonal group on the last subconstituent and computes their lengths, advancing understanding of these algebraic and combinatorial structures.

Findings

All suborbits of the point-stabilizer are classified.

Lengths of each suborbit are explicitly calculated.

Connections to quasi-strongly regular graphs and association schemes are established.

Abstract

As one of the serial papers on suborbits of point stabilizers in classical groups on the last subconstituent of dual polar graphs, the corresponding problem for orthogonal dual polar graphs over a finite field of odd characteristic is discussed in this paper. We determine all the suborbits of a point-stabilizer in the orthogonal group on the last subconstituent, and calculate the length of each suborbit. Moreover, we discuss the quasi-strongly regular graphs and the association schemes based on the last subconstituent, respectively.