Radicals of S n -invariant positive semidefinite hermitian forms
Algebraic Combinatorics, Volume 1 (2018) no. 4, p. 425-440
Let G be a finite group, V a complex permutation module for G over a finite G-set 𝒳, and f:V×V a G-invariant positive semidefinite hermitian form on V. In this paper we show how to compute the radical V of f, by extending to nontransitive actions the classical combinatorial methods from the theory of association schemes. We apply this machinery to obtain a result for standard Majorana representations of the symmetric groups.
Received : 2017-08-03
Revised : 2018-06-04
Accepted : 2018-06-10
Published online : 2018-09-10
DOI : https://doi.org/10.5802/alco.24
Classification:  20C30,  15A63,  05E25,  11E39
Keywords: Hermitian form, Symmetric group, Majorana representation, Monster group, Association scheme, Specht module.
@article{ALCO_2018__1_4_425_0,
     author = {Franchi, Clara and Ivanov, Alexander A. and Mainardis, Mario},
     title = {Radicals of $S\_n$-invariant positive semidefinite hermitian forms},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {1},
     number = {4},
     year = {2018},
     pages = {425-440},
     doi = {10.5802/alco.24},
     zbl = {06963900},
     language = {en},
     url = {https://alco.centre-mersenne.org/item/ALCO_2018__1_4_425_0}
}
Franchi, Clara; Ivanov, Alexander A.; Mainardis, Mario. Radicals of $S_n$-invariant positive semidefinite hermitian forms. Algebraic Combinatorics, Volume 1 (2018) no. 4, pp. 425-440. doi : 10.5802/alco.24. https://alco.centre-mersenne.org/item/ALCO_2018__1_4_425_0/

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