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.
Radicals of $S_n$-invariant positive semidefinite hermitian forms
Mainardis, Mario
2018-01-01
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.File in questo prodotto:
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