Geometric and homological properties of affine Deligne-Lusztig varieties

• Autores: Xuhua He
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 179, Nº 1, 2014, págs. 367-404
• Idioma: inglés
• DOI: 10.4007/annals.2014.179.1.6
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• Resumen

  • This paper studies affine Deligne-Lusztig varieties X w ~ (b) in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of X w ~ (b) for a minimal length element w ~ in the conjugacy class of an extended affine Weyl group. We then provide a reduction method that relates the structure of X w ~ (b) for arbitrary elements w ~ in the extended affine Weyl group to those associated with minimal length elements. Based on this reduction, we establish a connection between the dimension of affine Deligne-Lusztig varieties and the degree of the class polynomial of affine Hecke algebras. As a consequence, we prove a conjecture of Görtz, Haines, Kottwitz and Reuman