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An Algorithm for Computing Invariant Projectors in Representations of Wreath Products

  • Vladimir V. KornyakEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11661)

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.

Keywords

Wreath product Irreducible decomposition Invariant projectors Multipartite quantum system 

Notes

Acknowledgments

I am grateful to Yu.A. Blinkov for help in preparing the article and V.P. Gerdt for fruitful discussions and valuable advice.

Supplementary material

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia

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