Universal deformation rings for the symmetric group S_5 and one of its double covers

Abstract

Let $S_5$ denote the symmetric group on 5 letters, and let ${\hat{S}}_5$ denote a non-trivial double cover of $S_5$ whose Sylow 2-subgroups are generalized quaternion. We determine the universal deformation rings $R(S_5,V)$ and $R({\hat{S}}_5,V)$ for each mod 2 representation $V$ of $S_5$ that belongs to the principal 2-modular block of $S_5$ and whose stable endomorphism ring is given by scalars when it is inflated to ${\hat{S}}_5$. 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 $S_5$ and ${\hat{S}}_5$, respectively, has an affirmative answer.

10 pages, 5 figures; the proof of Theorem 1.1(a) has been shortened

References in corpus (2)

• Universal deformation rings and dihedral defect groups
• Universal deformation rings and dihedral 2-groups

Cited by in corpus (5)

• Universal deformation rings of modules over Frobenius algebras
• On Universal Deformation Rings for Gorenstein Algebras
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• On Singular Equivalences of Morita Type and Universal Deformation Rings for Gorenstein Algebras
• Universal deformation rings for a class of self-injective special biserial algebras