Universal deformation rings for the symmetric group S₅ and one of its double covers

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• 作者：Frauke M. Bleher ; Jennifer B. Froelich
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2011
• 出版时间：April 2011
• 年：2011
• 卷：215
• 期：4
• 页码：523-530
• 全文大小：266 K

文摘

Let S₅ denote the symmetric group on 5 letters, and let denote a non-trivial double cover of S₅ whose Sylow 2-subgroups are generalized quaternion groups. We determine the universal deformation rings R(S₅,V) and of each mod 2 representation V of S₅ that belongs to the principal 2-modular block of S₅ and whose stable endomorphism ring is given by scalars when it is inflated to . We show that for these V, a question raised by the first author and Chinburg concerning the relation of the universal deformation ring of V to the Sylow 2-subgroups of S₅ and , respectively, has an affirmative answer.