Affine Deligne¨CLusztig varieties associated to additive affine Weyl group elements

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• 作者：E.T.  ; Beazley ;   ; ^{etb1@williams.edu}
• 关键词：Affine Deligne&ndash ; Lusztig variety ; Affine Weyl group ; Elliptic/cuspidal conjugacy class ; Fully commutative element ; Loop group
• 刊名：Journal of Algebra
• 出版年：2012
• 出版时间：1 January 2012
• 年：2012
• 卷：349
• 期：1
• 页码：63-79
• 全文大小：237 K

文摘

Affine Deligne¨CLusztig varieties can be thought of as affine analogs of classical Deligne¨CLusztig varieties, or Frobenius-twisted analogs of Schubert varieties. We provide a method for proving a non-emptiness statement for affine Deligne¨CLusztig varieties inside the affine flag variety associated to affine Weyl group elements satisfying a certain length additivity hypothesis. In particular, we prove that non-emptiness holds whenever it is conjectured to do so for alcoves in the shrunken dominant Weyl chamber, providing a partial converse to the emptiness results of G?rtz, Haines, Kottwitz, and Reuman. Our technique involves the work of Geck and Pfeiffer on cuspidal conjugacy classes, in addition to an analysis of the combinatorics of certain fully commutative elements in the finite Weyl group.