Hi GAP team, I noticed the following description here [1]:
``` A representation V of a finite group G over an algebraically closed field K of characteristic zero is faithful (as a representation) if and only if every irreducible representation of G occurs as a subrepresentation of SnV (the n-th symmetric power of the representation V) for a sufficiently high n. Also, V is faithful (as a representation) if and only if every irreducible representation of G occurs as a subrepresentation of V ⊗ n = V ⊗ V ⊗ ⋯ ⊗ V ⏟ n times (the n-th tensor power of the representation V) for a sufficiently high n. ``` The meaning is very abstract and obscure to read and understand, so I want to know if I can work out simple and intuitive examples in GAP to verify the properties of faithful representation depicted above. [1] https://en.wikipedia.org/wiki/Faithful_representation Regards -- Assoc. Prof. Hongsheng Zhao <hongyi.z...@gmail.com> Theory and Simulation of Materials Hebei Vocational University of Technology and Engineering No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
