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EnglishLet 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]
| Autori: | ||
| Titolo: | Standard Majorana representations of the symmetric groups | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10801-016-0668-8 | |
| Data di pubblicazione: | 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. | |
| Lingua: | Inglese | |
| Rivista: | ||
| Citazione: | 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] | |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
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