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The unitary dual for the multiplicative group of arbitrary division algebras over local fields
Author:
Lawrence Corwin
Journal:
J. Amer. Math. Soc. 2 (1989), 565-598
MSC:
Primary 22E50; Secondary 11S40
MathSciNet review:
984512
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
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Colin
J. Bushnell and Albrecht
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Springer-Verlag, Berlin, 1983. MR 701540
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Corwin, Representations of division algebras over local
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MR
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Corwin, Representations of division algebras over local fields.
II, Pacific J. Math. 101 (1982), no. 1,
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Corwin, Approximation of prime elements in division algebras over
local fields and unitary representations of the multiplicative group,
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-, Supercuspidal representations of
, -adic, preprint.
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over a -adic field, preprint.
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Deligne, D.
Kazhdan, and M.-F.
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𝐺𝑙_{𝑛}, Pacific J. Math. 73
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, the product of two primes, 1988, preprint.
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MR
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-
- [1]
- C. Bushnell and A. Fröhlich, Gauss sums and
-adic division algebras, Lecture Notes in Math., no. 987, Springer, Berlin and New York, 1983. MR 701540 (84m:12017) - [2]
- H. Carayol, Représentations cuspidales du groupe linéaire, Ann. Sci. École Norm. Sup. (4) 17 (1984), 191-226. MR 760676 (86f:22019)
- [3]
- L. Corwin, Representations of division algebras over local fields, Adv. in Math. 13 (1974), 259-267. MR 0347780 (50:281)
- [4]
- -, Representations of division algebras over local fields. II, Pacific J. Math. 101 (1982), 49-70. MR 671839 (84b:12023)
- [5]
- -, Approximation of prime elements in division algebras over local fields and unitary representations of the multiplicative group, Pacific J. Math. 130 (1987), 223-251. MR 914100 (89c:11173)
- [6]
- -, Supercuspidal representations of
, -adic, preprint. - [7]
- L. Corwin, A. Moy, and P. J. Sally, Jr., Degrees and formal degrees for division algebras and
over a -adic field, preprint. - [8]
- P. Deligne, D. Kazhdan, and M. F. Vigneras, Représentations des algébras centrales simples
-adiques, Représentations des Groupes Réductif sur un Corps Local, Hermann, Paris, 1984, pp. 33-117. MR 771672 (86h:11044) - [9]
- P. Gerardin, Construction de series discrétes
-adiques, Lecture Notes in Math., no. 462, Springer, Berlin and New York, 1972. MR 0396859 (53:719) - [10]
- R. Howe, Representation theory for division algebras over local fields (tamely ramified case), Bull. Amer. Math. Soc. 77 (1971), 1063-1066. MR 0286939 (44:4146)
- [11]
- -, Kirillov theory for compact
-adic groups, Pacific J. Math. 73 (1977), 365-381. MR 0579176 (58:28314) - [12]
- -, Tamely ramified supercuspidal representations of
, Pacific J. Math. 73 (1977), 437-459. MR 0492087 (58:11241) - [13]
- H. Koch, Eisenteinsche Polynomfolgen and Arithmetik in Divisionsalgebren über lokalen Körpern, Math. Nachr. 104 (1981), 229-251. MR 657895 (84d:12015)
- [14]
- -, Zur Arithmetik in Divisionsalgebren über lokalen Körpern, Math. Nachr. 100 (1981), 9-19. MR 632618 (83a:12028)
- [15]
- P. Kutzko and D. Manderscheid, On the supercuspidal representations of
, the product of two primes, 1988, preprint. - [16]
- G. W. Mackey, Induced representations of groups, Amer. J. Math. 73 (1951), 576-592. MR 0042420 (13:106d)
- [17]
- A. Moy, Local constants and the tame Langlands correspondence, Amer. J. Math. 108 (1986), 863-930. MR 853218 (88b:11081)
- [18]
- A. Weil, Basic number theory, Springer, Berlin and New York, 1967. MR 0234930 (38:3244)
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Additional Information
Lawrence Corwin
Affiliation:
DOI:
http://dx.doi.org/10.1090/S0894-0347-1989-0984512-1
PII:
S 0894-0347(1989)0984512-1
Article copyright:
© Copyright 1989 American Mathematical Society
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