On the construction of tame supercuspidal representations

TL;DR

This paper revisits Yu's construction of supercuspidal representations for tamely ramified reductive groups over non-archimedean fields, providing a new proof of supercuspidality and correcting previous errors in the literature.

Contribution

It offers a new perspective and proof that the constructed representations are supercuspidal, and corrects a typo-related error in Yu's original work.

Findings

Confirmed supercuspidality of Yu's representations with a new proof

Provided a counterexample to previous propositions in Yu's 2001 paper

Clarified the construction process for 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.