-adic Whittaker functions and vector bundles on flag manifolds
Compositio Mathematica (1993)
- Volume: 85, Issue: 1, page 9-36
- ISSN: 0010-437X
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topReeder, Mark. "$p$-adic Whittaker functions and vector bundles on flag manifolds." Compositio Mathematica 85.1 (1993): 9-36. <http://eudml.org/doc/90194>.
@article{Reeder1993,
author = {Reeder, Mark},
journal = {Compositio Mathematica},
keywords = {split reductive groups; unramified principal series representations; Whittaker models; global sections; line bundles; flag manifolds; Iwahori fixed vectors; Lefschetz traces; cohomology groups of sheaves; maximal -split torus},
language = {eng},
number = {1},
pages = {9-36},
publisher = {Kluwer Academic Publishers},
title = {$p$-adic Whittaker functions and vector bundles on flag manifolds},
url = {http://eudml.org/doc/90194},
volume = {85},
year = {1993},
}
TY - JOUR
AU - Reeder, Mark
TI - $p$-adic Whittaker functions and vector bundles on flag manifolds
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 85
IS - 1
SP - 9
EP - 36
LA - eng
KW - split reductive groups; unramified principal series representations; Whittaker models; global sections; line bundles; flag manifolds; Iwahori fixed vectors; Lefschetz traces; cohomology groups of sheaves; maximal -split torus
UR - http://eudml.org/doc/90194
ER -
References
top- [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. Zbl0167.21703MR232406
- [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. Zbl0412.22015MR579172
- [BT] R. Bott, Homogeneous vector bundles, Ann. Math.66 (1957), 203-247. Zbl0094.35701MR89473
- [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. Zbl0421.22010MR546593
- [C1] W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups (unpublished manuscript).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. Zbl0472.22004MR571057
- [C-S] W. Casselman and J. Shalika, The unramified principal series of p-adic groups II., Comp. Math.41 (1980), 207-231. Zbl0472.22005MR581582
- [DM] M. Demazure, A very simple proof of Bott's theorem, Inven. Math.33 (1976), 271-272. Zbl0383.14017MR414569
- [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. Zbl0228.20015
- [Li] J.-S. Li, Some results on the unramified principal series of p-adic groups (preprint). MR1157324
- [K-L] D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math.87 (1987), 153-215. Zbl0613.22004MR862716
- [K] G. Kempf, The Grothendieck-Cousin complex of an induced representation, Adv. Math.29 (1978), 310-396. Zbl0393.20027MR509802
- [Ke] C.D. Keys, On the decomposition of reducible principal series representations of p-adic Chevalley groups, Pac. Jn. Math.101 (1982), 351-388. Zbl0438.22010MR675406
- [L] G. Lusztig, Affine Hecke algebras and their graded version, Jn. AMS2 (1989), 599-635. Zbl0715.22020MR991016
- [M] I.G. Macdonald, The Poincaré series of a Coxeter group, Math. Ann.199 (1972), 161-174. Zbl0286.20062MR322069
- [R] M. Reeder, On certain Iwahori invariants in the unramified principal series, Pac. Jn. Math. (to appear). Zbl0804.22010MR1151565
- [R1] M. Reeder, Old forms on GL(n), Amer. Jn. Math. vol. 113 (1991), 911-930. Zbl0758.11027MR1129297
- [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. Zbl0287.22016MR354942
- [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. Zbl0662.22011MR946277
- [Rog] J. Rogawski, On modules over the Hecke algebra of a p -adic group, Invent. Math.79 (1985), 443-465. Zbl0579.20037MR782228
- [S] T. Shintani, On an explicit formula for class-1 Whittaker functions, Proc. Japan Acad.52 (1976), 180-182. Zbl0387.43002MR407208
Citations in EuDML Documents
top- Mark Reeder, On the Iwahori-spherical discrete series for -adic Chevalley groups; formal degrees and -packets
- J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, F. Shahidi, On lifting from classical groups to
- William Casselman, Freydoon Shahidi, On irreducibility of standard modules for generic representations
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