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Representations on a complete discrete valuation ring. (Représentations sur un anneau de valuation discrète complet.) (French) Zbl 1178.20040
Summary: Following the first author [Rend. Semin. Mat. Univ. Padova 109, 45-62 (2003; Zbl 1048.20032)], we prove some results on the graphs of extensions attached to a representation on a complete discrete valuation ring with uniformizing parameter \(\pi\). On the one hand, under the assumption of residual multiplicity \(1\), we give a combinatorial description of all the graphs of extensions modulo \(\pi\) which appear. On the other hand, we prove a connexity result for the graph of all extensions modulo \(\pi^n\), which for \(n=1\) gives back the main result of [loc. cit.].

MSC:
20G05 Representation theory for linear algebraic groups
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11S23 Integral representations
20G25 Linear algebraic groups over local fields and their integers
20C11 \(p\)-adic representations of finite groups
51E24 Buildings and the geometry of diagrams
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