Dimensions of Some Affine Deligne-lusztig Varieties Les Dimensions De Certaines Variétés De Deligne-lusztig Affines

نویسندگان

  • ULRICH GÖRTZ
  • THOMAS J. HAINES
  • ROBERT E. KOTTWITZ
  • DANIEL C. REUMAN
  • D. C. REUMAN
چکیده

This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties Xμ(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of superbasic b. In the affine flag manifold, we prove a formula that reduces the dimension question for Xx(b) with b in the split torus to computations of dimensions of intersections of Iwahori orbits with orbits of the unipotent radical. Calculations using this formula allow us to verify a conjecture of Reuman in many new cases, and to make progress toward a generalization of his conjecture. Cet article concerne les dimensions de certaines variétés de Deligne-Lusztig affines, dans la Grassmannienne affine et dans la variété de drapeaux affine. Rapoport a conjecturé une formule pour les dimensions des variétés Xμ(b) dans la Grassmannienne affine. On prouve cette conjecture pour b dans le tore déployé; on trouve que ces variétés sont équi-dimensionnel; et on réduit la conjecture générale au cas où b est ”superbasic”. Dans le cas de la variété de drapeaux affine, on prouve une formule qui réduit la détermination de la dimension de Xx(b) avec b dans le tore déployé au calcul de dimensions d’intersections d’orbites de l’Iwahori avec d’orbites du radical unipotent. En utilisant cette formule on vérifie une conjecture de Reuman dans beaucoup de cas nouveaux, et on généralise sa conjecture.

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تاریخ انتشار 2005