## Duke Mathematical Journal

### On the tempered spectrum of quasi-split classical groups

#### Article information

Source
Duke Math. J. Volume 92, Number 2 (1998), 255-294.

Dates
First available: 19 February 2004

http://projecteuclid.org/euclid.dmj/1077231485

Mathematical Reviews number (MathSciNet)
MR1612785

Zentralblatt MATH identifier
0938.22014

Digital Object Identifier
doi:10.1215/S0012-7094-98-09206-7

#### Citation

Goldberg, David; Shahidi, Freydoon. On the tempered spectrum of quasi-split classical groups. Duke Mathematical Journal 92 (1998), no. 2, 255--294. doi:10.1215/S0012-7094-98-09206-7. http://projecteuclid.org/euclid.dmj/1077231485.

#### References

• [1] J. Arthur, The local behaviour of weighted orbital integrals, Duke Math. J. 56 (1988), no. 2, 223–293.
• [2] J. Arthur, Unipotent automorphic representations: conjectures, Astérisque (1989), no. 171-172, 13–71.
• [3] J. Arthur, Unipotent automorphic representations: global motivation, Automorphic forms, Shimura varieties, and $L$-functions, Vol. I (Ann Arbor, MI, 1988) eds. L. Clozel and J. S. Milne, Perspect. Math., vol. 10, Academic Press, Boston, MA, 1990, pp. 1–75.
• [4] I. N. Bernšteĭ n and A. V. Zelevinskiĭ, Representations of the group $GL(n,F),$ where $F$ is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5–70.
• [5] A. Borel, Automorphic $L$-functions, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61.
• [6] L. Clozel, Characters of nonconnected, reductive $p$-adic groups, Canad. J. Math. 39 (1987), no. 1, 149–167.
• [7] L. Clozel, Invariant harmonic analysis on the Schwartz space of a reductive $p$-adic group, Harmonic analysis on reductive groups (Brunswick, ME, 1989) eds. W. Barker and P. Sally, Progr. Math., vol. 101, Birkhäuser Boston, Boston, MA, 1991, pp. 101–121.
• [8] D. Goldberg, Some results on reducibility for unitary groups and local Asai $L$-functions, J. Reine Angew. Math. 448 (1994), 65–95.
• [9] D. Goldberg, Reducibility of induced representations for $\rm Sp(2n)$ and $\rm SO(n)$, Amer. J. Math. 116 (1994), no. 5, 1101–1151.
• [10] Harish-Chandra, Harmonic analysis on reductive $p$-adic groups, Lecture Notes in Math., vol. 162, Springer-Verlag, Berlin, 1970, Notes by G. van Dijk.
• [11] Harish-Chandra, Harmonic analysis on reductive $p$-adic groups, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), Amer. Math. Soc., Providence, R.I., 1973, pp. 167–192.
• [12] D. Kazhdan, Cuspidal geometry of $p$-adic groups, J. Analyse Math. 47 (1986), 1–36.
• [13] R. Kottwitz and D. Shelstad, Twisted endoscopy, II: Basic global theory, preprint.
• [14] R. Kottwitz and D. Shelstad, twisted endoscopy, I: Definitions, norm mappings, and transfer factors, preprint.
• [15] R. Kottwitz and J. D. Rogawski, The distributions in the invariant trace formula are supported on characters, preprint.
• [16] R. P. Langlands and D. Shelstad, On the definition of transfer factors, Math. Ann. 278 (1987), no. 1-4, 219–271.
• [17] O. T. O'Meara, Introduction to quadratic forms, Die Grundlehren der mathematischen Wissenschaften, Bd. 117, Academic Press Inc., Publishers, New York, 1963.
• [18] I. Satake, Classification theory of semi-simple algebraic groups, Lecture Notes in Pure and Appl. Math., vol. 3, Marcel Dekker Inc., New York, 1971.
• [19] F. Shahidi, On certain $L$-functions, Amer. J. Math. 103 (1981), no. 2, 297–355.
• [20] F. Shahidi, A proof of Langlands' conjecture on Plancherel measures; complementary series for $p$-adic groups, Ann. of Math. (2) 132 (1990), no. 2, 273–330.
• [21] F. Shahidi, Twisted endoscopy and reducibility of induced representations for $p$-adic groups, Duke Math. J. 66 (1992), no. 1, 1–41.
• [22] F. Shahidi, The notion of norm and the representation theory of orthogonal groups, Invent. Math. 119 (1995), no. 1, 1–36.
• [23] S. Shokranian, Geometric expansion of the local twisted trace formula, preprint.
• [24] A. J. Silberger, Introduction to harmonic analysis on reductive $p$-adic groups, Mathematical Notes, vol. 23, Princeton University Press, Princeton, N.J., 1979.