Gram-Schmidt-Vaserstein generators for odd sized elementary groups

TL;DR

This paper introduces a new set of generators for odd-sized elementary groups using Vaserstein's Gram-Schmidt process, enhancing understanding of their structure and providing tools for algebraic computations.

Contribution

It presents a novel application of Vaserstein's Gram-Schmidt process to generate elementary matrices in odd-sized groups, expanding the algebraic toolkit.

Findings

Provides explicit generators for odd-sized elementary groups.

Connects Gram-Schmidt process with group generation.

Simplifies the construction of elementary matrices.

Abstract

The Gram-Schmidt process of L.N. Vaserstein for making an elementary matrix symplectic yields a nice set of generators for the odd sized elementary group.