p -adic Whittaker functions and vector bundles on flag manifolds

Mark Reeder

Compositio Mathematica (1993)

  • Volume: 85, Issue: 1, page 9-36
  • ISSN: 0010-437X

How to cite

top

Reeder, 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
  1. [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
  2. [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
  3. [BT] R. Bott, Homogeneous vector bundles, Ann. Math.66 (1957), 203-247. Zbl0094.35701MR89473
  4. [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
  5. [C1] W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups (unpublished manuscript). 
  6. [C] W. Casselman, The unramified principal series of p-adic groups I., Comp. Math.40 (1980), 387-406. Zbl0472.22004MR571057
  7. [C-S] W. Casselman and J. Shalika, The unramified principal series of p-adic groups II., Comp. Math.41 (1980), 207-231. Zbl0472.22005MR581582
  8. [DM] M. Demazure, A very simple proof of Bott's theorem, Inven. Math.33 (1976), 271-272. Zbl0383.14017MR414569
  9. [G] V. Ginsburg, Deligne-Langlands conjecture and representations of affine Hecke algebras (preprint). 
  10. [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
  11. [Li] J.-S. Li, Some results on the unramified principal series of p-adic groups (preprint). MR1157324
  12. [K-L] D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math.87 (1987), 153-215. Zbl0613.22004MR862716
  13. [K] G. Kempf, The Grothendieck-Cousin complex of an induced representation, Adv. Math.29 (1978), 310-396. Zbl0393.20027MR509802
  14. [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
  15. [L] G. Lusztig, Affine Hecke algebras and their graded version, Jn. AMS2 (1989), 599-635. Zbl0715.22020MR991016
  16. [M] I.G. Macdonald, The Poincaré series of a Coxeter group, Math. Ann.199 (1972), 161-174. Zbl0286.20062MR322069
  17. [R] M. Reeder, On certain Iwahori invariants in the unramified principal series, Pac. Jn. Math. (to appear). Zbl0804.22010MR1151565
  18. [R1] M. Reeder, Old forms on GL(n), Amer. Jn. Math. vol. 113 (1991), 911-930. Zbl0758.11027MR1129297
  19. [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
  20. [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
  21. [Rog] J. Rogawski, On modules over the Hecke algebra of a p -adic group, Invent. Math.79 (1985), 443-465. Zbl0579.20037MR782228
  22. [S] T. Shintani, On an explicit formula for class-1 Whittaker functions, Proc. Japan Acad.52 (1976), 180-182. Zbl0387.43002MR407208

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.