Alcove walks and nearby cycles on affine flag manifolds
Ulrich Görtz
Mathematisches Institut Beringstr. 1 53115 Bonn Germany
DOI: 10.1007/s10801-007-0063-6
Abstract
Using Ram's theory of alcove walks we give a proof of the Bernstein presentation of the affine Hecke algebra. The method works also in the case of unequal parameters. We also discuss how these results help in studying sheaves of nearby cycles on affine flag manifolds.
Pages: 415–430
Full Text: PDF
References
1. Björner, A., Brenti, F.: Combinatorics of Coxeter Groups, Springer Graduate Texts in Mathematics, vol. 231 (2005)
2. Bourbaki, N.: Groupes et Algèbres de Lie. Chapters IV-VI. Masson, Paris (1981)
3. Bruhat, F., Tits, J.: Groupes réductifs sur un corps local I. Inst. Ht. Études Sci. Publ. Math. 41, 5-251 (1972)
4. Gaitsgory, D.: Construction of central elements in the affine Hecke algebra via nearby cycles. Invent. Math. 144, 253-280 (2001)
5. Görtz, U., Haines, T.: The Jordan-Hölder series for nearby cycles on some Shimura varieties and affine flag varieties, J. Reine Angew. Math. (to appear), math.AG/0402143
6. Görtz, U., Haines, T.: Bounds on weights of nearby cycles and Wakimoto sheaves on affine flag manifolds. Manuscr. Math. 120(4), 347-358 (2006)
7. Görtz, U., Haines, T., Kottwitz, R., Reuman, D.: Dimensions of some affine Deligne-Lusztig varieties. Ann. Sci. de l'E.N.S. 4 Sér. 39, 467-511 (2006)
8. Gaussent, S., Littelmann, P.: LS galleries, the path model, and MV cycles. Duke Math. J. 127(1), 35-88 (2005)
9. Haines, T., Kottwitz, R., Prasad, A.: Iwahori-Hecke algebras, math.RT/0309168
10. Haines, T., Ngô, B.C.: Nearby cycles for local models of some Shimura varieties. Compos. Math. 133, 117-150 (2002) J Algebr Comb (2007) 26: 415-430
2. Bourbaki, N.: Groupes et Algèbres de Lie. Chapters IV-VI. Masson, Paris (1981)
3. Bruhat, F., Tits, J.: Groupes réductifs sur un corps local I. Inst. Ht. Études Sci. Publ. Math. 41, 5-251 (1972)
4. Gaitsgory, D.: Construction of central elements in the affine Hecke algebra via nearby cycles. Invent. Math. 144, 253-280 (2001)
5. Görtz, U., Haines, T.: The Jordan-Hölder series for nearby cycles on some Shimura varieties and affine flag varieties, J. Reine Angew. Math. (to appear), math.AG/0402143
6. Görtz, U., Haines, T.: Bounds on weights of nearby cycles and Wakimoto sheaves on affine flag manifolds. Manuscr. Math. 120(4), 347-358 (2006)
7. Görtz, U., Haines, T., Kottwitz, R., Reuman, D.: Dimensions of some affine Deligne-Lusztig varieties. Ann. Sci. de l'E.N.S. 4 Sér. 39, 467-511 (2006)
8. Gaussent, S., Littelmann, P.: LS galleries, the path model, and MV cycles. Duke Math. J. 127(1), 35-88 (2005)
9. Haines, T., Kottwitz, R., Prasad, A.: Iwahori-Hecke algebras, math.RT/0309168
10. Haines, T., Ngô, B.C.: Nearby cycles for local models of some Shimura varieties. Compos. Math. 133, 117-150 (2002) J Algebr Comb (2007) 26: 415-430