On the construction of tame supercuspidal representations

Abstract

Let F be a non-archimedean local field of odd residual characteristic. 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 [Yu01], whose proofs relied on a typo in a reference.

16 pages; Section 4 rewritten. For an analogous construction of cuspidal representations with modular coefficients see arXiv:1905.06374v3

References in corpus (1)

• Types for tame p-adic groups

Cited by in corpus (6)

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• Hecke algebras for tame supercuspidal types
• On certain supercuspidal representations of symplectic groups associated with tamely ramified extensions : the formal degree conjecture and the root number conjecture