 Descent of an irreducible SL2 representation to PGL2 (source code)

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= Descent of an irreducible SL2 representation to PGL2
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The irreducible rational representations of $SL_2(\mathbb C)$ are $\operatorname{Sym}^n(\mathbb C^2)$. Such a representation descends through $SL_2\to PGL_2$ exactly when the central element $-I$ acts trivially, which holds exactly when $n$ is even.

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