J an 2 00 6 Counting Close Vertices in the Affine Buildings of SL n ( F ) and Sp n ( F )
نویسنده
چکیده
For a local field F with finite residue field, we count close vertices in the affine buildings of SLn(F ) and Spn(F ), addressing a question of [6]. In the case of SLn(F ), we give an explicit formula for the number ωn of vertices close to a given vertex. We establish the conjecture following Proposition 3.4 of [6] relating ωn and the number of chambers containing a given vertex. We give analogous results for Spn(F ) for special vertices.
منابع مشابه
2 00 5 Counting Close Vertices in the Affine Buildings of SL n ( F ) and Sp n ( F )
For a local field F with finite residue field, we count close vertices in the affine buildings of SLn(F ) and Spn(F ), addressing a question of [4]. In the case of SLn(F ), we give an explicit formula for the number ωn of vertices close to a given vertex. We establish the conjecture following Proposition 3.4 of [4] relating ωn and the number of chambers containing a given vertex. We give analog...
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For a local field F with finite residue field, we count close vertices in the affine buildings of SLn(F ) and Spn(F ), addressing a question raised in [4]. In the case of SLn(F ), we give an explicit formula for the number ωn of vertices close to a given vertex. We establish the conjecture following Proposition 3.4 of [4] relating ωn and the number of chambers containing a given vertex. We give...
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