Geodesic
An algorithm for decomposition of finite group representations by means of invariant projectors
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 228-248 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We describe an algorithm for decomposition of 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 projection into these subspaces. This allows us to reduce the problem to solving systems of quadratic equations. The current implementation of the proposed algorithm allows us to split representationы of dimensions up to hundreds of thousands. Computational examples are given. 
@article{ZNSL_2018_468_a15,
     author = {V. V. Kornyak},
     title = {An algorithm for decomposition of finite group representations by means of invariant projectors},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {228--248},
     year = {2018},
     volume = {468},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a15/}
}
TY  - JOUR
AU  - V. V. Kornyak
TI  - An algorithm for decomposition of finite group representations by means of invariant projectors
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 228
EP  - 248
VL  - 468
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a15/
LA  - ru
ID  - ZNSL_2018_468_a15
ER  - 
%0 Journal Article
%A V. V. Kornyak
%T An algorithm for decomposition of finite group representations by means of invariant projectors
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 228-248
%V 468
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a15/
%G ru
%F ZNSL_2018_468_a15
V. V. Kornyak. An algorithm for decomposition of finite group representations by means of invariant projectors. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 228-248. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a15/

[1] D. F. Holt, B. Eick, E. A. O'Brien, Handbook of Computational Group Theory, Chapman Hall/CRC, 2005 | MR | Zbl

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

[3] V. V. Kornyak, “Quantum models based on finite groups”, J. Phys. Conf. Ser., 965 (2018), 012023 ; http://stacks.iop.org/1742-6596/965/i=1/a=012023 | DOI

[4] V. V. Kornyak, “Modeling Quantum Behavior in the Framework of Permutation Groups”, EPJ Web of Conferences, 173 (2018), 01007 | DOI

[5] P. J. Cameron, Permutation Groups, Cambridge University Press, 1999 | MR | Zbl

[6] V. V. Kornyak, “Splitting Permutation Representations of Finite Groups by Polynomial Algebra Methods”, CASC 2018, LNCS, 11077, eds. Gerdt V., Koepf W., Seiler W., Vorozhtsov E., Springer, Cham, 2018, 304–318 | Zbl

[7] R. Wilson, Atlas of finite group representations, http://brauer.maths.qmul.ac.uk/Atlas/v3

[8] W. Bosma, J. Cannon, C. Playoust, A. Steel, Solving Problems with Magma, , University of Sydney, 2006 http://magma.maths.usyd.edu.au/magma/pdf/examples.pdf