Applications of the Wall form to unipotent isometries of index two

TL;DR

This paper explores the Wall form associated with unipotent isometries of index two in orthogonal groups, providing a decomposition and examining its relation to Clifford algebra invariants in characteristic two.

Contribution

It introduces a new decomposition method for unipotent index two isometries and analyzes their Wall form in relation to Clifford algebra invariants in characteristic two.

Findings

Decomposition of unipotent index two isometries.

Relation between Wall form and Clifford algebra invariants.

Insights into orthogonal group structures in characteristic two.

Abstract

We investigate the Wall form of unipotent elements of index two in the orthogonal group and obtain a decomposition for these elements. Also, in characteristic two, the relation between the Wall form and some invariants of the induced involution on the Clifford algebra is studied.