This little factoid from algebra quals stumped me: Let $G$ be a finite group and $H \triangleleft G$ an index $2$ subgroup. If we take an irreducible complex representation $V$ of $G$ and restrict it to $H$, it may not remain irreducible. However, show that the restriction of an irreducible representation is irreducible if any two elements in $H$ which are conjugate in $G$ remain conjugate in $H$.
2026-04-07 09:20:12.1775553612
Restricting a representation to a subgroup
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