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On a lemma of Ribet. (A propos d’un lemme de Ribet.) (French) Zbl 1048.20032
Let $$R$$ be a discrete complete valuation ring, $$K$$ its fraction field, $$k$$ the residue field, and $$V$$ an $$n$$-dimensional $$K$$-vector space. Consider an irreducible representation $$\rho\colon G\to\text{GL}(V)$$ of a group $$G$$ which stabilizes a lattice $$\Lambda\subset V$$; this defines a representation $$\overline\rho\colon G\to\text{GL}(n,k)$$. The main result of this paper consists in finding extensions between factors of $$\overline\rho$$. The case $$n=2$$ is an important lemma of K. A. Ribet [Invent. Math. 34, 151-162 (1976; Zbl 0338.12003)].

##### MSC:
 20G25 Linear algebraic groups over local fields and their integers 20G05 Representation theory for linear algebraic groups