Formulas for tamely ramified supercuspidal characters of 𝐺𝐿₃

Takahashi, Tetsuya

doi:10.1090/S0002-9947-02-03099-4

Formulas for tamely ramified supercuspidal characters of $\operatorname {GL}_3$
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Trans. Amer. Math. Soc. 355 (2003), 567-591 Request permission

Abstract:

Let $F$ denote a $p$-adic local field of residual characteristic $p\ne 3$. This article gives formulas, valid on the regular elliptic set, for the irreducible supercuspidal characters of $\operatorname {GL}_3(F)$ which correspond to characters of a ramified Cartan subgroup. In the case in which $F$ does not contain cube roots of unity, i.e., the case in which ramified cubic extensions of degree $3$ over $F$ cannot be Galois, base change results concerning “simple types" due to Bushnell and Henniart (1996) are used in the proofs.

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