Visualizing the Dickson-Siegel-Eichler-Roy elementary orthogonal group (Q6608214)

In his paper [J. Algebra 10, 286--298 (1968; Zbl 0181.04302)], \textit{A. Roy} introduced certain orthogonal transformations that generalized the classical Eichler-Siegel transformations and studied the cancellation problem in the theory of quadratic forms. The group generated by these orthogonal transformations is known as Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group.\N\NIn this paper, the authors define the Vaserstein-type generators \(L(v)\) and \(R(v)\), where \(v\in R^{n+2m-1}\) and \(R\) is a commutative ring with the unity for the DSER elementary orthogonal group (see Definition 3.2. from the paper for details). Then they prove the following main result: \N\NThe group generated by the matrices \(L(v)\) and \(R(v)\) (\(v\in R^{n+2m-1}\)) and the DSER elementary orthogonal group are conjugate subgroups of \(GL_{n+2m}(R)\).\N\NThis visualization of DSER elementary orthogonal transformations in terms of Vaserstein-type generators helps to understand the generators of the DSER elementary orthogonal group in a better way.