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Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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Book Information

Author(s): Colin J. Bushnell and Philip C. Kutzko
Title: The admissible dual of $\mathrm{GL}(N)$ via compact open subgroups
Additional book information: Princeton University Press, Princeton, NJ, 1993, ix + 313 pp., US$59.50. ISBN 0-691-03256-4

References:

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C. J. Bushnell, Hereditary orders, Gauss sums and supercuspidal representations of GL$ _{N}$, J. Reine Angew. Math. 375/376 (1987), 184-210. MR 882297 (88e:22024)

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H. Carayol, Représentations cuspidales du groupe linéaire, Ann. Sci. École Norm. Sup (4) 17 (1984), 191-225. MR 760676 (86f:22019)

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G. Henniart, Représentations des groupes réductifs p-adiques, Sém. Bourbaki, no. 736, Astérisque 201-202-203 (1991), 193-219. MR 1157843 (93b:22031)

[H1]
R. Howe, Tamely ramified supercuspidal representations of GL$ _{n}$, Pacific J. Math. 73 (1977), 437-460. MR 0492087 (58:11241)

[H2]
-, Some qualitative results on the representation theory of GL$ _{n}$ over a p-adic field, Pacific J. Math. 73 (1977), 479-538. MR 0492088 (58:11242)

[H3]
-, Classification of irreducible representations of GL$ _{2}(F)$ (F a local field), Inst. Hautes Études Sci., preprint, 1978.

[HM1]
R. Howe and A. Moy, Harish-Chandra homomorphisms for p-adic groups, CBMS Regional Conf. Ser. in Math., vol. 59, Amer. Math. Soc., Providence, RI, 1985. MR 821216 (87h:22023)

[HM2]
-, Minimal K-types for GL$ (n)$ over a p-adic field, Astérisque 171-172 (1989), 257-273.

[IM]
N. Iwahori and H. Matsumoto, On some decomposition and the structure of the Hecke rings of the p-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5-48. MR 0185016 (32:2486)

[KL]
D.Kazhdan and G. Lusztig, Proof of the Deligne--Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), 153-215. MR 862716 (88d:11121)

[K]
P. C. Kutzko, On the supercuspidal representation of GL$ _{2}$. II, Amer. J. Math. 100 (1978), 705-716. MR 0507254 (58:22411b)

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F. I. Mautner, Spherical functions over p-adic fields. I, II, Amer. J. Math. 80 (1958), 441-457; 86 (1964), 171-200. MR 0093558 (20:82)

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A. Moy, A conjecture on minimal K types for GL$ _{n}$ over a p-adic field, Contemp. Math., vol. 86, Amer. Math. Soc., Providence, RI, 1989, pp. 249-254. MR 987030

[R]
F. Rodier, Représentations de GL$ (n,k)$ où k est un corps p-adique, Sém. Bourbaki, no. 587, Astérisque 92-93 (1982), 201-218. MR 689531 (84h:22040)

[Wa]
J.-L. Waldspurger, Algebres de Hecke et induites de représentations cuspidales, pour GL$ _{n}$, J. Reine Angew. Math. 370 (1986), 127-191. MR 852514 (87m:22048)

Additional Information:

Reviewer(s):
Lawrence Morris

Review Information:
Journal: Bull. Amer. Math. Soc. 30 (1994), 295-301.
DOI: 10.1090/S0273-0979-1994-00472-0
PII: S 0273-0979(1994)00472-0




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