Irreducible Modular Representations of a Reductive p-Adic Group and Simple Modules for Hecke Algebras
Irreducible Modular Representations of a Reductive p-Adic Group and Simple Modules for Hecke Algebras
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约简p进群的不可约模表示和赫克代数的简单模
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
N. Onland
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文献类型：
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作者：
Renée M G Verdiesen;C. V. van Gils;R. Stellato;W. Verschuren;F. Broekmans;A. C. de Kat;Y. T. van der Schouw;N. Onland
设F是剩余特征为p的局部非阿基米德域，G是定义在F上的连通约化群的有理点群。寻找G的不可约复表示的分类的两个要点是试图证明任何不可约尖点表示都是从开紧子群导出的，并且对于一类Hecke代数，具有给定惯性尖点支撑的不可约表示可以用简单的模来分类。在一个非复域的特征向量的域R上，出现了新的严重困难，本文的目的是指出一种避免这些困难的方法。当群是GL（n，F）时使用的镜像技巧并不推广，但我们的新方法是通用的，我们可以将Morris和Moy-Prasad关于0级表示的结果从复情形扩展到R。
Let F be a local non-archimedean field of residual characteristic p, and let G be the group of rational points of a connected reductive group defined over F. The two main points in the search for a classification of the irreducible complex representations of G is to try to prove that any irreducible cuspidal representation is induced from an open compact subgroup and that the irreducible representations with a given inertial cuspidal support are classified by simple modules for the Hecke algebra of a type. Over a field R of characteristic ≠ p which is not the complex field, new serious difficulties arise and the purpose of this article is to indicate a way to avoid them. The mirabolic trick used when the group is GL(n, F) does not generalize, but our new method is general and we can extend from the complex case to R the results of Morris and Moy—Prasad for level 0 representations.