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REDUCED NOTATION, INNER PLETHYSMS AND THE SYMMETRICAL GROUP

Abstract : The reduced notation for irreducible representations of the symmetric group S-n is interpreted in terms of symmetric formal series and vertex operators, and is used to prove a number of properties of reduced Kronecker products and inner plethysms in an n-independent manner. Conditions for self-associativity of Kronecker products and inner plethysms are established. Reduced inner plethysms are developed and applied to the question of non-simple phase groups among the symmetric S-n and alternating A(n) groups.
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Contributor : Jean-Yves Thibon <>
Submitted on : Wednesday, May 2, 2012 - 5:53:22 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:06 PM

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T Scharf, Jean-Yves Thibon, Bg Wybourne. REDUCED NOTATION, INNER PLETHYSMS AND THE SYMMETRICAL GROUP. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 1993, 26 (24), pp.7461--7478. ⟨10.1088/0305-4470/26/24/019⟩. ⟨hal-00693537⟩

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