Abstract:
Let G≀SN be the wreath product of a finite group G and the symmetric group SN. The aim of this paper is to prove the branching theorem for the increasing sequence of finite groups G≀S1⊂G≀S2⊂⋯⊂G≀SN⊂… and the analog of Young's orthogonal form for this case, using the inductive approach, invented by A. Vershik and A. Okounkov for the case of symmetric group.
Citation:
I. A. Pushkarev, “On the representation theory of wreath products of finite group and symmetric group”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Zap. Nauchn. Sem. POMI, 240, POMI, St. Petersburg, 1997, 229–244; J. Math. Sci. (New York), 96:5 (1999), 3590–3599
\Bibitem{Pus97}
\by I.~A.~Pushkarev
\paper On the representation theory of wreath products of finite group and symmetric group
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~II
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 240
\pages 229--244
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl475}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1691647}
\zmath{https://zbmath.org/?q=an:0959.20015}
\transl
\jour J. Math. Sci. (New York)
\yr 1999
\vol 96
\issue 5
\pages 3590--3599
\crossref{https://doi.org/10.1007/BF02175835}
Linking options:
https://www.mathnet.ru/eng/znsl475
https://www.mathnet.ru/eng/znsl/v240/p229
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L. Poulain d'Andecy, “Fusion Procedure for Wreath Products of Finite Groups by the Symmetric Group”, Algebr Represent Theor, 17:3 (2014), 809
O. V. Ogievetskii, L. Poulain d'Andecy, “An inductive approach to representations of complex reflection groups
$G(m,1,n)$”, Theoret. and Math. Phys., 174:1 (2013), 95–108
Wan J., “Wreath Hecke algebras and centralizer construction for wreath products”, Journal of Algebra, 323:9 (2010), 2371–2397
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Jinkui Wan, Weiqiang Wang, “Modular Representations and Branching Rules for Wreath Hecke Algebras”, International Mathematics Research Notices, 2008 (2008)
Adin R.M., Brenti F., Roichman Yu., “A construction of Coxeter group representations (II)”, J Algebra, 306:1 (2006), 208–226
A. M. Vershik, A. Yu. Okounkov, “A new approach to the representation theory of the symmetric groups. II”, J. Math. Sci. (N. Y.), 131:2 (2005), 5471–5494
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