Purity of equivalued affine Springer fibers

Goresky, Mark; Kottwitz, Robert; MacPherson, Robert

doi:10.1090/S1088-4165-06-00200-7

Purity of equivalued affine Springer fibers
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by Mark Goresky, Robert Kottwitz and Robert MacPherson

Represent. Theory 10 (2006), 130-146

DOI: https://doi.org/10.1090/S1088-4165-06-00200-7

Published electronically: February 20, 2006

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Abstract:

The affine Springer fiber corresponding to a regular integral equivalued semisimple element admits a paving by vector bundles over Hessenberg varieties and hence its homology is “pure".

References

Jeffrey D. Adler, Refined anisotropic $K$-types and supercuspidal representations, Pacific J. Math. 185 (1998), no. 1, 1–32. MR 1653184, DOI 10.2140/pjm.1998.185.1
Yuri Berest, Pavel Etingof, and Victor Ginzburg, Finite-dimensional representations of rational Cherednik algebras, Int. Math. Res. Not. 19 (2003), 1053–1088. MR 1961261, DOI 10.1155/S1073792803210205
Roman Bezrukavnikov, The dimension of the fixed point set on affine flag manifolds, Math. Res. Lett. 3 (1996), no. 2, 185–189. MR 1386839, DOI 10.4310/MRL.1996.v3.n2.a5
Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
C. De Concini, G. Lusztig, and C. Procesi, Homology of the zero-set of a nilpotent vector field on a flag manifold, J. Amer. Math. Soc. 1 (1988), no. 1, 15–34. MR 924700, DOI 10.1090/S0894-0347-1988-0924700-2
C. Kenneth Fan, Euler characteristic of certain affine flag varieties, Transform. Groups 1 (1996), no. 1-2, 35–39. MR 1390748, DOI 10.1007/BF02587734
Mark Goresky, Robert Kottwitz, and Robert MacPherson, Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math. 131 (1998), no. 1, 25–83. MR 1489894, DOI 10.1007/s002220050197
Mark Goresky, Robert Kottwitz, and Robert Macpherson, Homology of affine Springer fibers in the unramified case, Duke Math. J. 121 (2004), no. 3, 509–561. MR 2040285, DOI 10.1215/S0012-7094-04-12135-9
D. Kazhdan and G. Lusztig, Fixed point varieties on affine flag manifolds, Israel J. Math. 62 (1988), no. 2, 129–168. MR 947819, DOI 10.1007/BF02787119
Bertram Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 973–1032. MR 114875, DOI 10.2307/2372999
R. P. Langlands, Les débuts d’une formule des traces stable, Publications Mathématiques de l’Université Paris VII [Mathematical Publications of the University of Paris VII], vol. 13, Université de Paris VII, U.E.R. de Mathématiques, Paris, 1983 (French). MR 697567

Sur le lemme fondamental pour les groupes unitaires

Sur le lemme fondamental pour les groupes unitaires: le cas totalement ramifié et homogène

math.RT/0309132

G. Lusztig and J. M. Smelt, Fixed point varieties on the space of lattices, Bull. London Math. Soc. 23 (1991), no. 3, 213–218. MR 1123328, DOI 10.1112/blms/23.3.213
Allen Moy and Gopal Prasad, Unrefined minimal $K$-types for $p$-adic groups, Invent. Math. 116 (1994), no. 1-3, 393–408. MR 1253198, DOI 10.1007/BF01231566
F. De Mari, C. Procesi, and M. A. Shayman, Hessenberg varieties, Trans. Amer. Math. Soc. 332 (1992), no. 2, 529–534. MR 1043857, DOI 10.1090/S0002-9947-1992-1043857-6
Daniel S. Sage, The geometry of fixed point varieties on affine flag manifolds, Trans. Amer. Math. Soc. 352 (2000), no. 5, 2087–2119. MR 1491876, DOI 10.1090/S0002-9947-99-02295-3
Jean-Pierre Serre, Corps locaux, Publications de l’Université de Nancago, No. VIII, Hermann, Paris, 1968 (French). Deuxième édition. MR 0354618
E. Sommers, A family of affine Weyl group representations, Transform. Groups 2 (1997), no. 4, 375–390. MR 1486037, DOI 10.1007/BF01234541
T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 167–266. MR 0268192
Eric Vasserot, Induced and simple modules of double affine Hecke algebras, Duke Math. J. 126 (2005), no. 2, 251–323. MR 2115259, DOI 10.1215/S0012-7094-04-12623-5
Jiu-Kang Yu, Construction of tame supercuspidal representations, J. Amer. Math. Soc. 14 (2001), no. 3, 579–622. MR 1824988, DOI 10.1090/S0894-0347-01-00363-0