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An Algorithm for Decomposing Representations of Finite Groups Using Invariant Projections

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We describe an algorithm for decomposing permutation representations of finite groups over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in invariant subspaces are operators of projecting to these subspaces. This allows us to reduce the problem to solving systems of quadratic equations. The current implementation of the suggested algorithm allows us to split representations with dimensions up to hundreds of thousands. Computational examples are given.

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References

  1. D. F. Holt, B. Eick, and E. A. O’Brien, Handbook of Computational Group Theory, Chapman & Hall/CRC (2005).

  2. R. Parker, “The computer calculation of modular characters (the Meat-Axe),” in: M. D. Atkinson (ed.), Computational Group Theory, Academic Press, London (1984), pp. 267–274.

  3. V. V. Kornyak, “Quantum models based on finite groups,” J. Phys.: Conf. Ser., 965, 012023 (2018).

    Google Scholar 

  4. V. V. Kornyak, “Modeling quantum behavior in the framework of permutation groups,” EPJ Web of Conferences, 173, 01007 (2018).

    Article  Google Scholar 

  5. P. J. Cameron, Permutation Groups, Cambridge Univ. Press (1999).

  6. V. V. Kornyak, “Splitting permutation representations of finite groups by polynomial algebra methods,” in: V. Gerdt, W. Koepf, W. Seiler, and E. Vorozhtsov (eds.), CASC 2018, Lect. Notes Comput. Sci., 11077, Springer, Cham (2018), pp. 304–318.

  7. R. Wilson et al., “Atlas of finite group representations,” http://brauer.maths.qmul.ac.uk/Atlas/v3.

  8. W. Bosma, J. Cannon, C. Playoust, and A. Steel, “Solving problems with Magma,” http://magma.maths.usyd.edu.au/magma/pdf/examples.pdf.

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Authors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia

    V. V. Kornyak

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  1. V. V. Kornyak
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Correspondence to V. V. Kornyak.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 468, 2018, pp. 228–248.

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Kornyak, V.V. An Algorithm for Decomposing Representations of Finite Groups Using Invariant Projections. J Math Sci 240, 651–664 (2019). https://doi.org/10.1007/s10958-019-04382-y

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  • DOI: https://doi.org/10.1007/s10958-019-04382-y

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