Minuscule alcoves for GLn and GSp2n
- Cite this article as:
- Kottwitz, R. & Rapoport, M. manuscripta math. (2000) 102: 403. doi:10.1007/s002290070034
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Let μ be a minuscule coweight for either GLn or GSp2n, and regard μ as an element tμ in the extended affine Weyl group \(\). We say that an element \(\) is μ-admissible if there exists μ′ in the Weyl group orbit of μ such that x≤tμ′ in the Bruhat order on \(\). Our main result is that \(\) is μ-admissible if and only if it is μ-permissible, where μ-permissibility is defined using inequalities arising naturally in the study of bad reduction of Shimura varieties.