Let G be a finite group, W be a ℝ[G]-module equipped with a G-invariant positive definite bilinear form (,)_W, and X a finite generating set of W such that X is transitively permuted by G. We show a new method for computing the dimensions of the irreducible constituents of W. Further, we apply this method to Majorana representations of the symmetric groups and prove that the symmetric group S_n has a Majorana representation in which every permutation of type (2, 2) of S_n corresponds to a Majorana axis if and only if n≤12 .

Standard Majorana representations of the symmetric groups

MAINARDIS, Mario
2016

Abstract

Let G be a finite group, W be a ℝ[G]-module equipped with a G-invariant positive definite bilinear form (,)_W, and X a finite generating set of W such that X is transitively permuted by G. We show a new method for computing the dimensions of the irreducible constituents of W. Further, we apply this method to Majorana representations of the symmetric groups and prove that the symmetric group S_n has a Majorana representation in which every permutation of type (2, 2) of S_n corresponds to a Majorana axis if and only if n≤12 .
File in questo prodotto:
File Dimensione Formato  
JACO-D-15-00027_R2-2.pdf

non disponibili

Descrizione: Bozza finale
Tipologia: Documento in Post-print
Licenza: Non pubblico
Dimensione 873.39 kB
Formato Adobe PDF
873.39 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1098504
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact