Affine Deligne–Lusztig varieties associated to additive affine Weyl group elements
| Autor: | Elizabeth T. Beazley |
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| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Weyl group Pure mathematics Loop group Algebra and Number Theory Elliptic/cuspidal conjugacy class Affine Deligne–Lusztig variety Fully commutative element Affine geometry symbols.namesake Mathematics::Algebraic Geometry Affine representation Affine Weyl group Affine hull Affine group symbols Affine space Affine transformation Affine variety Mathematics::Representation Theory Mathematics |
| Zdroj: | Journal of Algebra. 349(1):63-79 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2011.10.020 |
| Popis: | Affine Deligne–Lusztig varieties can be thought of as affine analogs of classical Deligne–Lusztig varieties, or Frobenius-twisted analogs of Schubert varieties. We provide a method for proving a non-emptiness statement for affine Deligne–Lusztig 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 Gortz, 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. |
| Databáze: | OpenAIRE |
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