Let be a finite group, a complex permutation module for over a finite -set , and a -invariant positive semidefinite hermitian form on . In this paper we show how to compute the radical of , 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.
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.24
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},
pages = {425--440},
publisher = {MathOA foundation},
volume = {1},
number = {4},
year = {2018},
doi = {10.5802/alco.24},
mrnumber = {3875072},
zbl = {06963900},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/alco.24/}
}
TY - JOUR AU - Franchi, Clara AU - Ivanov, Alexander A. AU - Mainardis, Mario TI - Radicals of $S_n$-invariant positive semidefinite hermitian forms JO - Algebraic Combinatorics PY - 2018 SP - 425 EP - 440 VL - 1 IS - 4 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.24/ DO - 10.5802/alco.24 LA - en ID - ALCO_2018__1_4_425_0 ER -
%0 Journal Article %A Franchi, Clara %A Ivanov, Alexander A. %A Mainardis, Mario %T Radicals of $S_n$-invariant positive semidefinite hermitian forms %J Algebraic Combinatorics %D 2018 %P 425-440 %V 1 %N 4 %I MathOA foundation %U http://archive.numdam.org/articles/10.5802/alco.24/ %R 10.5802/alco.24 %G en %F 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. http://archive.numdam.org/articles/10.5802/alco.24/
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