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
2016-01-01

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 .
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1098504
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