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GH from MO
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If $G$ is the real points of a semisimple algebraic group and $\rho:G\mapsto GL(n,\mathbb R)$$\rho:G\to GL(n,\mathbb R)$ is continuous representation. Is $\rho$ an algebraic morphism?

If $G$ is the real points of a semisimple algebraic group and $\rho:G\mapsto GL(n,\mathbb R)$ is continuous representation. Is $\rho$ an algebraic morphism?

If $G$ is the real points of a semisimple algebraic group and $\rho:G\to GL(n,\mathbb R)$ is continuous representation. Is $\rho$ an algebraic morphism?

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Jerry
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Do representations of real semisimple algebraic group have to be algebraic?

If $G$ is the real points of a semisimple algebraic group and $\rho:G\mapsto GL(n,\mathbb R)$ is continuous representation. Is $\rho$ an algebraic morphism?