The Conjecture of Kottwitz and Rapoport in the Case of Split Groups
نویسنده
چکیده
We prove a result involving root systems that implies a converse to Mazur’s inequality for all split groups, conjectured by Kottwitz and Rapoport (see [10]). This was previously known for classical groups (see [11]) and G2 (see [5]).
منابع مشابه
On a Conjecture of Kottwitz and Rapoport
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all split and quasi-split (connected) reductive groups. These results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.
متن کاملA Conjecture of Kottwitz and Rapoport for Split Groups
We prove a result involving root systems that implies a converse to Mazur’s inequality for all split groups, conjectured by Kottwitz and Rapoport (see e.g. [6]). This was previously known for classical groups (see e.g. [7]) and G2 (see e.g. [3]).
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This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties Xμ(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of...
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تاریخ انتشار 2008