An Algorithm for Computing Invariant Projectors in Representations of Wreath Products
Representation Theory
2020-06-19 v2 Symbolic Computation
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1906.00858,
title = {An Algorithm for Computing Invariant Projectors in Representations of Wreath Products},
author = {Vladimir V. Kornyak},
journal= {arXiv preprint arXiv:1906.00858},
year = {2020}
}
Comments
13 pages, version 2: computer outputs corrected