$p$-adic Whittaker functions and vector bundles on flag manifolds
Compositio Mathematica, Tome 85 (1993) no. 1, pp. 9-36.
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author = {Reeder, Mark},
title = {$p$-adic {Whittaker} functions and vector bundles on flag manifolds},
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Reeder, Mark. $p$-adic Whittaker functions and vector bundles on flag manifolds. Compositio Mathematica, Tome 85 (1993) no. 1, pp. 9-36. http://www.numdam.org/item/CM_1993__85_1_9_0/

[A-B] M.F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes: II applications, Ann. of Math. 88 (1968), 451-491. | MR 232406 | Zbl 0167.21703

[B-Z] I.N. Bernstein and A.V. Zelevinsky, Induced representations of reductive p-adic groups I, Ann. Sci. Ec. Norm. Sup. 10 (1977), 441-472. | Numdam | MR 579172 | Zbl 0412.22015

[BT] R. Bott, Homogeneous vector bundles, Ann. Math. 66 (1957), 203-247. | MR 89473 | Zbl 0094.35701

[Car] P. Cartier, Representations of p-adic groups: A survey, in: Automorphic forms, representations and L-functions, Proc. Symp. Pure Math., 1979, pp. 111-155. | MR 546593 | Zbl 0421.22010

[C1] W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups (unpublished manuscript).

[C] W. Casselman, The unramified principal series of p-adic groups I., Comp. Math. 40 (1980), 387-406. | Numdam | MR 571057 | Zbl 0472.22004

[C-S] W. Casselman and J. Shalika, The unramified principal series of p-adic groups II., Comp. Math. 41 (1980), 207-231. | Numdam | MR 581582 | Zbl 0472.22005

[DM] M. Demazure, A very simple proof of Bott's theorem, Inven. Math. 33 (1976), 271-272. | MR 414569 | Zbl 0383.14017

[G] V. Ginsburg, Deligne-Langlands conjecture and representations of affine Hecke algebras (preprint).

[I-M] N. Iwahori and H. Matsumoto, On some Bruhat decompositions and the structure of the Hecke ring of the p-adic groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5-48. | Numdam | Zbl 0228.20015

[Li] J.-S. Li, Some results on the unramified principal series of p-adic groups (preprint). | MR 1157324

[K-L] D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), 153-215. | MR 862716 | Zbl 0613.22004

[K] G. Kempf, The Grothendieck-Cousin complex of an induced representation, Adv. Math. 29 (1978), 310-396. | MR 509802 | Zbl 0393.20027

[Ke] C.D. Keys, On the decomposition of reducible principal series representations of p-adic Chevalley groups, Pac. Jn. Math. 101 (1982), 351-388. | MR 675406 | Zbl 0438.22010

[L] G. Lusztig, Affine Hecke algebras and their graded version, Jn. AMS 2 (1989), 599-635. | MR 991016 | Zbl 0715.22020

[M] I.G. Macdonald, The Poincaré series of a Coxeter group, Math. Ann. 199 (1972), 161-174. | MR 322069 | Zbl 0286.20062

[R] M. Reeder, On certain Iwahori invariants in the unramified principal series, Pac. Jn. Math. (to appear). | MR 1151565 | Zbl 0804.22010

[R1] M. Reeder, Old forms on GL(n), Amer. Jn. Math. vol. 113 (1991), 911-930. | MR 1129297 | Zbl 0758.11027

[Ro] F. Rodier, Whittaker models for admissible representations of real algebraic groups, in: Harmonic Analysis on Homogeneous Spaces, Proc. Symp. Pure Math., 1973, pp. 425-430. | MR 354942 | Zbl 0287.22016

[Ro2] F. Rodier, Sur les représentations non ramifiées des groupes reductifs p-adiques: l'exemple de GSp(4), Bull. Soc. Math. France, 116 (1988), 15-42. | Numdam | MR 946277 | Zbl 0662.22011

[Rog] J. Rogawski, On modules over the Hecke algebra of a p -adic group, Invent. Math. 79 (1985), 443-465. | MR 782228 | Zbl 0579.20037

[S] T. Shintani, On an explicit formula for class-1 Whittaker functions, Proc. Japan Acad. 52 (1976), 180-182. | MR 407208 | Zbl 0387.43002