The unitary dual for the multiplicative group of arbitrary division algebras over local fields
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- by Lawrence Corwin
- J. Amer. Math. Soc. 2 (1989), 565-598
- DOI: https://doi.org/10.1090/S0894-0347-1989-0984512-1
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References
- 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
- H. Carayol, Représentations cuspidales du groupe linéaire, Ann. Sci. École Norm. Sup. (4) 17 (1984), no. 2, 191–225 (French). MR 760676
- Lawrence Corwin, Representations of division algebras over local fields, Advances in Math. 13 (1974), 259–267. MR 347780, DOI 10.1016/0001-8708(74)90069-3
- Lawrence Corwin, Representations of division algebras over local fields. II, Pacific J. Math. 101 (1982), no. 1, 49–70. MR 671839
- Lawrence Corwin, Approximation of prime elements in division algebras over local fields and unitary representations of the multiplicative group, Pacific J. Math. 130 (1987), no. 2, 223–251. MR 914100 —, Supercuspidal representations of ${\text {G}}{{\text {L}}_{pp’}}(F)$, $F$ $p$-adic, preprint. L. Corwin, A. Moy, and P. J. Sally, Jr., Degrees and formal degrees for division algebras and ${\text {G}}{{\text {L}}_n}$ over a $p$-adic field, preprint.
- 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
- Paul Gérardin, Construction de séries discrètes $p$-adiques, Lecture Notes in Mathematics, Vol. 462, Springer-Verlag, Berlin-New York, 1975. Sur les séries discrètes non ramifiées des groupes réductifs déployés $p$-adiques. MR 0396859
- Roger Howe, Representation theory for division algebras over local fields (tamely ramified case), Bull. Amer. Math. Soc. 77 (1971), 1063–1066. MR 286939, DOI 10.1090/S0002-9904-1971-12867-7
- Roger E. Howe, Kirillov theory for compact $p$-adic groups, Pacific J. Math. 73 (1977), no. 2, 365–381. MR 579176
- Roger E. Howe, Tamely ramified supercuspidal representations of $\textrm {Gl}_{n}$, Pacific J. Math. 73 (1977), no. 2, 437–460. MR 492087
- Helmut Koch, Eisensteinsche Polynomfolgen und Arithmetik in Divisionsalgebren über lokalen Körpern, Math. Nachr. 104 (1981), 229–251 (German). MR 657895, DOI 10.1002/mana.19811040118
- Helmut Koch, Zur Arithmetik in Divisionsalgebren über lokalen Körpern, Math. Nachr. 100 (1981), 9–19 (German). MR 632618, DOI 10.1002/mana.19811000102 P. Kutzko and D. Manderscheid, On the supercuspidal representations of ${\text {G}}{{\text {L}}_N}$, $N$ the product of two primes, 1988, preprint.
- George W. Mackey, On induced representations of groups, Amer. J. Math. 73 (1951), 576–592. MR 42420, DOI 10.2307/2372309
- Allen Moy, Local constants and the tame Langlands correspondence, Amer. J. Math. 108 (1986), no. 4, 863–930. MR 853218, DOI 10.2307/2374518
- André Weil, Basic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 144, Springer-Verlag New York, Inc., New York, 1967. MR 0234930
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: J. Amer. Math. Soc. 2 (1989), 565-598
- MSC: Primary 22E50; Secondary 11S40
- DOI: https://doi.org/10.1090/S0894-0347-1989-0984512-1
- MathSciNet review: 984512