A Las Vegas Rewriting Algorithm for the Symmetric Square Representation of Classical Groups

TL;DR

This paper introduces a Las Vegas algorithm specifically designed for rewriting the Symmetric Square representation of classical groups, improving recognition processes by focusing on non-natural representations.

Contribution

It provides a specialized algorithm for the Symmetric Square representation, enhancing the efficiency of constructive recognition of classical groups.

Findings

The algorithm successfully rewrites the Symmetric Square representation.

It offers theoretical and practical improvements over generic methods.

The approach is probabilistic and guarantees correctness with high probability.

Abstract

In constructive recognition of a representation of a Classical group $G$, much attention has been paid to the natural representation as well as to generic (Black Box) algorithms that treat all representations uniformly. There are theoretical and practical improvements to be made by giving special treatment to certain non-natural representations that arise frequently. In this paper we present and analyse a Las Vegas algorithm for rewriting the Symmetric Square representation.