Dimensions of some affine Deligne-Lusztig varieties
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 39 (2006) no. 3, pp. 467-511.
@article{ASENS_2006_4_39_3_467_0,
     author = {G\"ortz, Ulrich and Haines, Thomas J. and Kottwitz, Robert E. and Reuman, Daniel C.},
     title = {Dimensions of some affine {Deligne-Lusztig} varieties},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {467--511},
     publisher = {Elsevier},
     volume = {Ser. 4, 39},
     number = {3},
     year = {2006},
     doi = {10.1016/j.ansens.2005.12.004},
     zbl = {1108.14035},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2005.12.004/}
}
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Görtz, Ulrich; Haines, Thomas J.; Kottwitz, Robert E.; Reuman, Daniel C. Dimensions of some affine Deligne-Lusztig varieties. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 39 (2006) no. 3, pp. 467-511. doi : 10.1016/j.ansens.2005.12.004. http://www.numdam.org/articles/10.1016/j.ansens.2005.12.004/

[1] Bruhat F., Tits J., Groupes réductifs sur un corps local. I, Inst. Hautes Études Sci. Publ. Math. 41 (1972) 5-251. | EuDML | Numdam | MR | Zbl

[2] Casselman W., Machine calculations in Weyl groups, Invent. Math. 116 (1994) 95-108. | EuDML | MR | Zbl

[3] Chai C.-L., Newton polygons as lattice points, Amer. J. Math. 122 (5) (2000) 967-990. | MR | Zbl

[4] Dabrowski R., Comparison of the Bruhat and the Iwahori decompositions of a p-adic Chevalley group, J. Algebra 167 (3) (1994) 704-723. | MR | Zbl

[5] Deligne P., La conjecture de Weil II, Inst. Hautes Études Sci. Publ. Math. 52 (1980). | EuDML | Numdam | MR | Zbl

[6] Demazure M., Gabriel P., Groupes Algébriques: Tome I. Géométrie algébrique-Généralités-Groupes commutatifs, Masson and CIE, Paris, 1970, 700 pp.+xxvi. | Zbl

[7] Dieudonné J., Groupes de Lie et hyperalgèbres de Lie sur un corps de caractéristique p>0. VII, Math. Ann. 134 (1957) 114-133. | EuDML | MR | Zbl

[8] Fargues L., Mantovan E., Variétés de Shimura, espaces de Rapoport-Zink et correspondances de Langlands locales, Astérisque 291 (2004). | Numdam | Zbl

[9] Haines T.J., On matrix coefficients of the Satake isomorphism: complements to the paper of Rapoport, Manuscripta Math. 101 (2000) 167-174. | MR | Zbl

[10] Haines T., Kottwitz R., Prasad A., Iwahori-Hecke algebras, math.RT/0309168.

[11] Kato S., Spherical functions and a q-analogue of Kostant's weight multiplicity formula, Invent. Math. 66 (1982) 461-468. | MR | Zbl

[12] Kottwitz R., Dimensions of Newton strata in the adjoint quotient of reductive groups, Pure Appl. Math. Q., in press, math.AG/0601196. | MR | Zbl

[13] Kottwitz R., Isocrystals with additional structure, Compositio Math. 56 (1985) 201-220. | Numdam | MR | Zbl

[14] Kottwitz R., Isocrystals with additional structure. II, Compositio Math. 109 (1997) 255-339. | MR | Zbl

[15] Kottwitz R., On the Hodge-Newton decomposition for split groups, Int. Math. Res. Not. 26 (2003) 1433-1447. | MR | Zbl

[16] Kottwitz R., Rapoport M., On the existence of F-crystals, Comment. Math. Helv. 78 (2003) 153-184, math.NT/0202229. | MR | Zbl

[17] Leigh Lucarelli C., A converse to Mazur's inequality for split classical groups, J. Inst. Math. Jussieu 3 (2) (2004) 165-183, math.NT/0211327. | MR | Zbl

[18] Lusztig G., Singularities, character formulas, and a q-analog of weight multiplicities, in: Analyse et topologie sur les espaces singuliers, I-II, (Luminy, 1981), Soc. Math. France, Paris, 1983, pp. 208-229. | Numdam | MR | Zbl

[19] Manin Y., Theory of commutative formal groups over fields of finite characteristic, Uspekhi Mat. Nauk 18 (6 (114)) (1963) 3-90, (in Russian); English translation in:, Russian Math. Surveys 18 (6) (1963) 1-83. | MR | Zbl

[20] Mantovan E., On the cohomology of certain PEL type Shimura varieties, Duke Math. J. 129 (3) (2005) 573-610. | MR | Zbl

[21] Matsumoto H., Analyse harmonique dans les systèmes de Tits bornologiques de type affine, Springer Lecture Notes, vol. 590, Springer, Berlin, 1977. | MR | Zbl

[22] Mirkovic I., Vilonen K., Geometric Langlands duality and representations of algebraic groups over commutative rings, math.RT/0401222v2.

[23] Mirkovic I., Vilonen K., Perverse sheaves on affine Grassmannians and Langlands duality, Math. Res. Lett. 7 (1) (2000) 13-24. | MR | Zbl

[24] Mumford D., The Red Book of Varieties and Schemes, Lecture Notes in Math., vol. 1358, Springer, Berlin, 1988. | MR | Zbl

[25] Ngô B.C., Polo P., Résolutions de Demazure affines et formule de Casselman-Shalika géométrique, J. Algebraic Geom. 10 (3) (2001) 515-547. | MR | Zbl

[26] Oort F., Foliations in moduli spaces of abelian varieties, J. Amer. Math. Soc. 17 (2) (2004) 267-296. | MR | Zbl

[27] Rapoport M., A positivity property of the Satake isomorphism, Manuscripta Math. 101 (2000) 153-166. | MR | Zbl

[28] Rapoport M., A guide to the reduction modulo p of Shimura varieties, Astérisque 298 (2005) 271-318, math.AG/0205022. | Numdam | MR | Zbl

[29] Rapoport M., Richartz M., On the classification and specialization of F-isocrystals with additional structure, Compositio Math. 103 (1996) 153-181. | Numdam | MR | Zbl

[30] Rapoport M., Zink T., Period Spaces for p-Divisible Groups, Ann. of Math. Stud., vol. 141, Princeton University Press, Princeton, NJ, 1996. | MR | Zbl

[31] Reuman D., Determining whether certain affine Deligne-Lusztig sets are non-empty, Thesis, Chicago, 2002, math.NT/0211434.

[32] Reuman D., Formulas for the dimensions of some affine Deligne-Lusztig varieties, Michigan Math. J. 52 (2) (2004) 435-451. | MR | Zbl

[33] Viehmann E., Moduli spaces of p-divisible groups, math.AG/0502320.

[34] Viehmann E., The dimension of some affine Deligne-Lusztig varieties, Annales Sci. de l'E.N.S. 39 (3) (2006), math.AG/0510385. | Numdam | MR | Zbl

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