# An Algorithm for Computing Invariant Projectors in Representations of Wreath Products

## TL;DR

This paper presents an algorithm to compute primitive orthogonal idempotents in the centralizer ring of wreath product representations, aiding decomposition into irreducible components, with applications in quantum mechanics.

## Contribution

It introduces a C implementation of an algorithm for decomposing high-dimensional wreath product representations into irreducible components.

## Key findings

- Algorithm successfully computes invariant projectors.
- C implementation handles high-dimensional representations.
- Examples demonstrate practical applicability.

## Abstract

We describe an algorithm for computing the complete set of primitive orthogonal idempotents in the centralizer ring of the permutation representation of a wreath product. This set of idempotents determines the decomposition of the representation into irreducible components. In the formalism of quantum mechanics, these idempotents are projection operators into irreducible invariant subspaces of the Hilbert space of a multipartite quantum system. The C implementation of the algorithm constructs irreducible decompositions of high-dimensional representations of wreath products. Examples of computations are given.