Fₚ-representations over p-fields

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Let p be a prime, k a finite extension of Fₚ of cardinal q, l a finite extension of k of group Σ=Gal(l|k), and T a subgroup of l×. Using the method of "little groups", we classify irreducible Fₚ-representations of the group G=T×qΣ, the twisted product of Σ with the Σ-module T. We then use these results to classify irreducible continuous Fₚ-representations of the profinite group of automorphisms Gal(K|K) of the maximal galoisian extension K of a local field K with residue field k.