Let G be a finite group, V a complex permutation module for G over a finite G-set X, and f:V×V→C 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.
Franchi, C., Ivanov, A. A., Mainardis, M., Radicals of Sn-invariant positive semidefinite hermitian forms, <<ALGEBRAIC COMBINATORICS>>, 2018; 1 (4): 425-440. [doi:10.5802/alco.24] [http://hdl.handle.net/10807/126367]
Radicals of Sn-invariant positive semidefinite hermitian forms
Franchi, Clara;
2018
Abstract
Let G be a finite group, V a complex permutation module for G over a finite G-set X, and f:V×V→C 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.
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