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arXiv 1208.4128math.GRmath.NT
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附录A:李型有限群表示的完备性

Appendix A: Adequacy of representations of finite groups of Lie type

Robert M. Guralnick

摘要:

索恩引入了适当表征的概念,作为对怀尔斯、泰勒和其他人使用的大表征的削弱。在Dieulefait的论文《Symm 5(GL(2))的自同构和基变换》的附录中,我们证明了SL(2,q)的某些表示是适当的。这是使用Dieulefait证明结果Hecke特征形的水平1和newforms。我们还证明了李型有限群表示在自然特征中的充分性的一些一般结果。

英文摘要:

Thorne introduced the notion of adequate representations as a weakening of the big representations used by Wiles and Taylor and others. In this appendix to Dieulefait's paper, Automorphy of Symm5(GL(2)) and base change, we show that certain representations of SL(2,q) are adequate. This is used by Dieulefait to prove results about Hecke eigenforms of level 1 and newforms. We also prove some general results about adequacy for representations of finite groups of Lie type in the natural characteristic.

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