A classification of irreducible admissible mod p representations of p-adic reductive groups
A classification of irreducible admissible mod p representations of p-adic reductive groups
复制标题
p进约简群的不可约容许模p表示的分类
DOI：
10.1090/jams/862
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
M. Vigneras
中科院分区：
文献类型：
--
作者：
N. Abe;G. Henniart;F. Herzig;M. Vigneras
设F是局部紧非阿基米德域，p是其剩余特征，G是F上的连通约化群。设C是特征为p的代数闭域，利用G = G（F）的Levi子群的超尖点C-表示和抛物归纳，给出了G = G（F）的不可约容许C-表示的完全分类.这样，我们就把第三位作者的观点推到它们的自然结论上，第三位作者处理了G = GL_m的情形，第一位作者处理了分裂群G，进一步扩展了第三位作者的观点。在分裂的情况下，我们首先得到一个分类的Levi子群的超奇异表示，并作为一个结果表明，超奇异性是相同的超尖性。
Let F be a locally compact non-archimedean field, p its residue characteristic, and G a connected reductive group over F. Let C an algebraically closed field of characteristic p. We give a complete classification of irreducible admissible C-representations of G = G(F), in terms of supercuspidal C-representations of the Levi subgroups of G, and parabolic induction. Thus we push to their natural conclusion the ideas of the third-named author, who treated the case G = GL_m, as further expanded by the first-named author, who treated split groups G. As in the split case, we first get a classification in terms of supersingular representations of Levi subgroups, and as a consequence show that supersingularity is the same as supercuspidality.