Abstract
This paper studies affine Deligne-Lusztig varieties $X_{\tilde w}(b)$ in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of $X_{\tilde w}(b)$ for a minimal length element $\tilde w$ in the conjugacy class of an extended affine Weyl group. We then provide a reduction method that relates the structure of $X_{\tilde w}(b)$ for arbitrary elements $\tilde w$ 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.
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JOURNAL = {Compositio Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {103},
YEAR = {1996},
NUMBER = {2},
PAGES = {153--181},
ISSN = {0010-437X},
CODEN = {CMPMAF},
MRCLASS = {14F30 (22E50)},
MRNUMBER = {1411570},
MRREVIEWER = {Abdellah Mokrane},
URL = {http://www.numdam.org/item?id=CM_1996__103_2_153_0},
ZBLNUMBER = {0874.14008},
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@book {Zb, MRKEY = {2717502},
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}