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.
Franchi, C., Ivanov, A. A., Mainardis, M., Standard Majorana representations of the symmetric groups, <<JOURNAL OF ALGEBRAIC COMBINATORICS>>, 2016; 44 (2): 265-292. [doi:10.1007/s10801-016-0668-8] [http://hdl.handle.net/10807/74443]
Standard Majorana representations of the symmetric groups
Franchi, ClaraPrimo
;
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.