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Tables of reductions of symmetrized inner products (``inner plethysms'') of ordinary irreducible representations of symmetric groups


Author: N. Esper
Journal: Math. Comp. 29 (1975), 1150-1151
MSC: Primary 20C30
DOI: https://doi.org/10.1090/S0025-5718-1975-0387398-1
MathSciNet review: 0387398
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Abstract: Decompositions of symmetrized inner products $ [\alpha ] \boxdot [\beta ]$ of ordinary irreducible representations $ [\alpha ]$ of symmetric groups $ {S_n}$ and $ [\beta ]$ of $ {S_m}$ were evaluated on a CDC 6400. Tables were obtained for $ 2 \leqslant n \leqslant 10$ and $ 2 \leqslant m \leqslant 5$ as well as for $ m = 6$ and $ 2 \leqslant n \leqslant 7$.


References [Enhancements On Off] (What's this?)

  • [1] N. ESPER, Ein interaktives Programmsystem zur Erzeugung der rationalisierten Charakterentafel einer endlichen Gruppe, Staatsexamensarbeit, Aachen, 1974. (To appear.)
  • [2] A. KERBER, "Symmetrization of representations," Proc. Second Internat. Colloq. Group Theoretical Methods in Physics, Nijmegen, June 1973.
  • [3] R. C. King, Branching rules for 𝐺𝐿(𝑁)⊃_{𝑚} and the evaluation of inner plethysms, J. Mathematical Phys. 15 (1974), 258–267. MR 0331999, https://doi.org/10.1063/1.1666632
  • [4] G. Ja. LJUBARSKIĬ, Group Theory and Its Applications to Physics, GITTL, Moscow, 1957; English transl., Pergamon Press, New York, 1960. MR 21 #5441; 22 #7709.

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DOI: https://doi.org/10.1090/S0025-5718-1975-0387398-1
Article copyright: © Copyright 1975 American Mathematical Society