Gaussian Elimination in Symplectic and split orthogonal groups

TL;DR

This paper develops a Gaussian elimination-like algorithm tailored for symplectic and orthogonal groups, enabling efficient computation of the spinor norm and double coset decompositions in computational group theory.

Contribution

It introduces a novel algorithm for symplectic and orthogonal groups with specific applications in computing the spinor norm and double coset decompositions.

Findings

Algorithm effectively computes the spinor norm.

Algorithm computes double coset decompositions.

Applications improve computational group theory methods.

Abstract

This paper studies an algorithm similar to that of Gaussian elimination in symplectic and orthogonal groups. We discuss two applications of this algorithm in computational group theory. One computes the spinor norm and the other computes the double coset decomposition with respect to Siegel maximal parabolic subgroup.