On the mod p reduction of orthogonal representations

TL;DR

This paper proves that the mod p reduction of orthogonal linear representations remains orthogonal and extends this property to algebra representations with involution, using the concept of middle lattices.

Contribution

It introduces a generalization of the orthogonality preservation under mod p reduction to algebra representations with involution, utilizing middle lattices.

Findings

Reduction mod p preserves orthogonality in linear representations.

Generalization to algebra representations with involution.

Use of middle lattices is essential in proofs.

Abstract

We show that the reduction mod p of an orthogonal linear representation is orthogonal, and we generalize this fact to representations of algebras with involution.The proofs make an essential use of the notion of " middle lattices ".