Transactions of the American Mathematical Society

On some constants in the supercuspidal characters of $\operatorname{GL}_l$ ,

a prime $\neq p$

Author(s): Tetsuya Takahashi
Journal: Trans. Amer. Math. Soc. 357 (2005), 2509-2526.
MSC (2000): Primary 22E50; Secondary 11F70
Posted: December 29, 2004
Retrieve article in: PDF DVI PostScript

Abstract: The article gives explicit values of some constants which appear in the character formula for the irreducible supercuspidal representation of $\operatorname{GL}_l(F)$ for

a local field of the residual characteristic $p\neq l$ .

1.: J. Arthur and L. Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Math. Studies 120, Princeton Univ. Press, 1989.MR 1007299 (90m:22041)
2.: A. Badulescu, Correspondance entre $\operatorname{GL}_n$ et ses formes intérieures en caractéristique positive, Thèse, Université de Paris-sud, Centre d'Orsay, 1999.
3.: C. J. Bushnell and A. Fröhlich, Gauss Sums and -adic Division Algebras, Lecture Notes in Math. 987, Springer, Berlin, 1983. MR 0701540 (84m:12017)
4.: C. J. Bushnell and G. Henniart, Local Tame Lifting For $\operatorname{GL}(N)$ I: Simple characters, Inst. Hautes Études Sci. Publ. Math. No. 83 (1996), 105-233. MR 1423022 (98m:11129)
5.: H. Carayol, Représentation cuspidales du groupe linéaire, Ann. Scient. Éc. Norm. Sup. 17 (1984), 191-226. MR 0760676 (86f:22019)
6.: L. Corwin and R. Howe, Computing characters of tamely ramified division algebras, Pac. J. Math. 73 (1977), 461-477. MR 0492084 (58:11238)
7.: L. Corwin, A. Moy and P. J. Sally, Jr., Supercuspidal character formulas for $\operatorname{GL}_l$ , Contemp. Math. 191, AMS, 1995, 1-11. MR 1365530 (96m:22037)
8.: S. M. Debacker, Supercuspidal characters of $\operatorname{GL}_l$ , a prime, Ph.D. thesis, Univ. of Chicago, 1997.
9.: S. M. Debacker and P. J. Sally, Jr., Germs, characters and the Fourier transforms of nilpotent orbits, The Mathematical Legacy of Harish-Chandra (Baltimore, MD, 1998), Proc. Sympos. Pure Math. 68, AMS, 2000, pp. 191-221. MR 1767897 (2001i:22022)
10.: P. Deligne, D. Kazhdan, and M.-F. Vinéras, Représentations des algèbres centrales simples -adiques, in: Représentations des Groupes Réductifs sur un Corps Local, Herman, Paris, 1984, pp. 33-117. MR 0771672 (86h:11044)
11.: R. Godement and H. Jacquet, Zeta functions of simple algebras, Lecture Notes in Math. 260, Springer, Berlin, 1972. MR 0342495 (49:7241)
12.: G. Henniart, Correspondance de Jaquet-Langlands explicite I : le cas modéré de degré premier in: Séminaire de Theórie des Nombres, Paris 1990-91, Progress in Math. 108, Birkhäuser, Basel, 1993, pp. 85-114. MR 1263525 (95d:11064)
13.: R. Howe, Kirillov theory for compact -adic groups, Pac. J. Math. 73, (1977), 365-381. MR 0579176 (58:28314)
14.: R. Howe, Tamely ramified supercuspidal representations of $\operatorname{GL}_n(F)$ , Pac. J. Math. 73 (1977), 437-460. MR 0492087 (58:11241)
15.: H. Hijikata, H. Saito, and M. Yamauchi, Representations of quaternion algebras over local fields and trace formula of Hecke operators, J. Number Theory 43 (1993), 123-167. MR 1207495 (94e:11126)
16.: P. Kutzko, Character formulas for supercuspidal representations of $\operatorname{GL}_l$ , a prime, Amer. J. Math. 109 (1987), 201-222. MR 0882420 (88k:22003)
17.: A. Moy, Local constant and the tame Langlands correspondence, Amer. J. Math. 108 (1986), 863-930. MR 0853218 (88b:11081)
18.: F. Murnaghan, Characters of supercuspidal representations of $\operatorname{SL}(n)$ , Pac. J. Math. 170 (1995), 217-235. MR 1359978 (96k:22030)
19.: F. Murnaghan, Characters of supercuspidal representations of classical groups, Ann. Sci. Éc. Norm. Sup. (4) 29 (1996), 49-105. MR 1368705 (98c:22016)
20.: F. Murnaghan, Local character expansions and Shalika germs for $\operatorname{GL}(n)$ , Math. Ann. 304 (1996), 423-455. MR 1375619 (98b:22020)
21.: H. Reimann, Representations of tamely ramified p-adic division and matrix algebras, J. Number Theory 38 (1991), 58-105. MR 1105671 (92h:11103)
22.: J. Rogawski, Representations of $\operatorname{GL}(n)$ and division algebras over -adic field, Duke Math. J. 50 (1983), 161-196. MR 0700135 (84j:12018)
23.: T. Takahashi, Characters of cuspidal unramified series for central simple algebras of prime degree, J. Math. Kyoto Univ. 32-4 (1992), 873-888. MR 1194118 (94e:11124)
24.: T. Takahashi, Character formula for representations of local quaternion algebras (Wildly ramified case), J. Math. Kyoto Univ. 36-1 (1996), 151-197. MR 1381546 (97f:11096)
25.: T. Takahashi, Formulas for tamely ramified supercuspidal characters of $\operatorname{GL}_3$ , Trans. Amer. Math. Soc. 355 (2003), no. 2, 567-591. MR 1932714 (2003i:22020)

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 22E50, 11F70

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

DOI: 10.1090/S0002-9947-04-03727-4
PII: S 0002-9947(04)03727-4
Keywords: Character, supercuspidal representation, Kloosterman sum
Received by editor(s): January 7, 2004
Posted: December 29, 2004
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS