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Forums
Mathematics
Linear and Abstract Algebra
Getting new irreducible representations from old ones
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[QUOTE="fresh_42, post: 6005889, member: 572553"] A standard method in case of linear representations on a real vectorspace ##V_\mathbb{R}## is to construct ##V_\mathbb{C} = V_\mathbb{R} \otimes_\mathbb{R} \mathbb{C}## and define for a given ##\varphi_\mathbb{R} \, : \,G \longrightarrow GL(V_\mathbb{R})## $$ \varphi_\mathbb{C} \, : \,G \longrightarrow GL(V_\mathbb{C}) \quad \text{ by } \quad \varphi_\mathbb{C}(g)(\lambda\cdot v) = \varphi_\mathbb{R}(g)(v) \otimes \lambda $$ I'm not sure, however, whether they automatically will be irreducible again, as there are simply more eigenvalues available, so I doubt it. [/QUOTE]
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Forums
Mathematics
Linear and Abstract Algebra
Getting new irreducible representations from old ones
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