Transactions of the American Mathematical Society

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Formulas for tamely ramified supercuspidal characters of $\operatorname{GL}_3$


Author: Tetsuya Takahashi
Journal: Trans. Amer. Math. Soc. 355 (2003), 567-591
MSC (2000): Primary 22E50; Secondary 11F70
Published electronically: October 4, 2002
MathSciNet review: 1932714
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Abstract: Let $F$ denote a $p$-adic local field of residual characteristic $p\ne3$. 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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Additional Information

Tetsuya Takahashi
Affiliation: Department of Mathematics and Information, College of Integrated Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho Sakai, 599-8531, Japan
Email: takahasi@mi.cias.osakafu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03099-4
Keywords: Characters, supercuspidal, base change
Received by editor(s): September 28, 1998
Received by editor(s) in revised form: May 2, 2002
Published electronically: October 4, 2002
Article copyright: © Copyright 2002 American Mathematical Society