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Irreducible modular representations of GL\(_ 2\) of a local field. (English) Zbl 0826.22019

Let \(F\) be a local field such that the characteristic of its residue field is nonzero, and let \(G = \text{GL}_2 (F)\). The authors give a classification of smooth irreducible representations of the group \(G\) by studying certain universal objects.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
11F70 Representation-theoretic methods; automorphic representations over local and global fields
20G05 Representation theory for linear algebraic groups
20G25 Linear algebraic groups over local fields and their integers
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