On some constants in the supercuspidal characters of $\operatorname {GL}_l$, $l$ a prime $\neq p$
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- by Tetsuya Takahashi
- Trans. Amer. Math. Soc. 357 (2005), 2509-2526
- DOI: https://doi.org/10.1090/S0002-9947-04-03727-4
- Published electronically: December 29, 2004
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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 $F$ a local field of the residual characteristic $p\neq l$.References
- James Arthur and Laurent Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies, vol. 120, Princeton University Press, Princeton, NJ, 1989. MR 1007299
- A. Badulescu, Correspondance entre $\operatorname {GL}_n$ et ses formes intérieures en caractéristique positive, Thèse, Université de Paris-sud, Centre d’Orsay, 1999.
- Colin J. Bushnell and Albrecht Fröhlich, Gauss sums and $p$-adic division algebras, Lecture Notes in Mathematics, vol. 987, Springer-Verlag, Berlin-New York, 1983. MR 701540, DOI 10.1007/BFb0066413
- Colin J. Bushnell and Guy Henniart, Local tame lifting for $\textrm {GL}(N)$. I. Simple characters, Inst. Hautes Études Sci. Publ. Math. 83 (1996), 105–233. MR 1423022, DOI 10.1007/BF02698646
- H. Carayol, Représentations cuspidales du groupe linéaire, Ann. Sci. École Norm. Sup. (4) 17 (1984), no. 2, 191–225 (French). MR 760676, DOI 10.24033/asens.1470
- Lawrence Corwin and Roger E. Howe, Computing characters of tamely ramified $p$-adic division algebras, Pacific J. Math. 73 (1977), no. 2, 461–477. MR 492084, DOI 10.2140/pjm.1977.73.461
- Lawrence Corwin, Allen Moy, and Paul J. Sally Jr., Supercuspidal character formulas for $\textrm {GL}_l$, Representation theory and harmonic analysis (Cincinnati, OH, 1994) Contemp. Math., vol. 191, Amer. Math. Soc., Providence, RI, 1995, pp. 1–11. MR 1365530, DOI 10.1090/conm/191/02321
- S. M. Debacker, Supercuspidal characters of $\operatorname {GL}_l$, $l$ a prime, Ph.D. thesis, Univ. of Chicago, 1997.
- Stephen DeBacker and Paul 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., vol. 68, Amer. Math. Soc., Providence, RI, 2000, pp. 191–221. MR 1767897, DOI 10.1090/pspum/068/1767897
- P. Deligne, D. Kazhdan, and M.-F. Vignéras, Représentations des algèbres centrales simples $p$-adiques, Representations of reductive groups over a local field, Travaux en Cours, Hermann, Paris, 1984, pp. 33–117 (French). MR 771672
- Roger Godement and Hervé Jacquet, Zeta functions of simple algebras, Lecture Notes in Mathematics, Vol. 260, Springer-Verlag, Berlin-New York, 1972. MR 0342495, DOI 10.1007/BFb0070263
- Guy Henniart, Correspondance de Jacquet-Langlands explicite. I. Le cas modéré de degré premier, Séminaire de Théorie des Nombres, Paris, 1990–91, Progr. Math., vol. 108, Birkhäuser Boston, Boston, MA, 1993, pp. 85–114 (French). MR 1263525
- Roger E. Howe, Kirillov theory for compact $p$-adic groups, Pacific J. Math. 73 (1977), no. 2, 365–381. MR 579176, DOI 10.2140/pjm.1977.73.365
- Roger E. Howe, Tamely ramified supercuspidal representations of $\textrm {Gl}_{n}$, Pacific J. Math. 73 (1977), no. 2, 437–460. MR 492087, DOI 10.2140/pjm.1977.73.437
- Hiroaki Hijikata, Hiroshi Saito, and Masatoshi Yamauchi, Representations of quaternion algebras over local fields and trace formulas of Hecke operators, J. Number Theory 43 (1993), no. 2, 123–167. MR 1207495, DOI 10.1006/jnth.1993.1013
- Philip Kutzko, Character formulas for supercuspidal representations of $\textrm {GL}_l,\;l$ a prime, Amer. J. Math. 109 (1987), no. 2, 201–221. MR 882420, DOI 10.2307/2374571
- Allen Moy, Local constants and the tame Langlands correspondence, Amer. J. Math. 108 (1986), no. 4, 863–930. MR 853218, DOI 10.2307/2374518
- Fiona Murnaghan, Characters of supercuspidal representations of $\textrm {SL}(n)$, Pacific J. Math. 170 (1995), no. 1, 217–235. MR 1359978, DOI 10.2140/pjm.1995.170.217
- Fiona Murnaghan, Characters of supercuspidal representations of classical groups, Ann. Sci. École Norm. Sup. (4) 29 (1996), no. 1, 49–105. MR 1368705, DOI 10.24033/asens.1735
- Fiona Murnaghan, Local character expansions and Shalika germs for $\textrm {GL}(n)$, Math. Ann. 304 (1996), no. 3, 423–455. MR 1375619, DOI 10.1007/BF01446300
- Harry Reimann, Representations of tamely ramified $p$-adic division and matrix algebras, J. Number Theory 38 (1991), no. 1, 58–105. MR 1105671, DOI 10.1016/0022-314X(91)90093-Q
- Jonathan D. Rogawski, Representations of $\textrm {GL}(n)$ and division algebras over a $p$-adic field, Duke Math. J. 50 (1983), no. 1, 161–196. MR 700135
- Tetsuya Takahashi, Characters of cuspidal unramified series for central simple algebras of prime degree, J. Math. Kyoto Univ. 32 (1992), no. 4, 873–888. MR 1194118, DOI 10.1215/kjm/1250519411
- Tetsuya Takahashi, Character formula for representations of local quaternion algebras (wildly ramified case), J. Math. Kyoto Univ. 36 (1996), no. 1, 151–197. MR 1381546, DOI 10.1215/kjm/1250518611
- Tetsuya Takahashi, Formulas for tamely ramified supercuspidal characters of $\textrm {GL}_3$, Trans. Amer. Math. Soc. 355 (2003), no. 2, 567–591. MR 1932714, DOI 10.1090/S0002-9947-02-03099-4
Bibliographic Information
- 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
- Received by editor(s): January 7, 2004
- Published electronically: December 29, 2004
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 357 (2005), 2509-2526
- MSC (2000): Primary 22E50; Secondary 11F70
- DOI: https://doi.org/10.1090/S0002-9947-04-03727-4
- MathSciNet review: 2140448