Geometric and homological properties of affine Deligne-Lusztig varieties

Details Geometric and homological properties of affine Deligne-Lusztig varieties Geometric and homological properties of affine Deligne-Lusztig varieties

2012-01-24

arxiv.org/abs/1201.4901v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

This paper studies affine Deligne-Lusztig variety $X_{\tw}(b)$ in the affine flag variety of a tamely ramified group. We describe the geometric structure of $X_{\tw}(b)$ for $\tw$ minimal length element in a conjugacy class of extended affine Weyl group, generalizing one of the main results in \cite{HL}. We then provide a reduction method relating $X_{\tw}(b)$ for arbitrary $\tw$ in the extended affine Weyl group to those associated to a minimal length element. Based on this, we establish a connection between the dimension of affine Deligne-Lusztig variety and the degree of class polynomial of affine Hecke algebra and as a consequence, prove a conjecture of G\"ortz, Haines, Kottwitz and Reuman in \cite{GHKR}.

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