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On the construction of tame supercuspidal representations
- Part of
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- Journal:
- Compositio Mathematica / Volume 157 / Issue 12 / December 2021
- Published online by Cambridge University Press:
- 03 January 2022, pp. 2733-2746
- Print publication:
- December 2021
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- Article
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Let
$F$ be a non-archimedean local field of residual characteristic 
$p \neq 2$. Let 
$G$ be a (connected) reductive group over 
$F$ that splits over a tamely ramified field extension of 
$F$. We revisit Yu's construction of smooth complex representations of 
$G(F)$ from a slightly different perspective and provide a proof that the resulting representations are supercuspidal. We also provide a counterexample to Proposition 14.1 and Theorem 14.2 in Yu [Construction of tame supercuspidal representations, J. Amer. Math. Soc. 14 (2001), 579–622], whose proofs relied on a typo in a reference.
