In the representation theory of $p$-adic reductive group, types for supercuspidal representations are important. For inner forms $G$ of $\mathrm{GL}_{N}$, as constructions of types for supercuspidal representations, Yu's construction and simple types mainly by Sécherre are known. In this talk, we compare these constructions. In particular, we show that in some assumption supercuspidal representations of $G$ obtained by Yu's construction are essentially tame in means of Bushnell-Henniart.

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