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For every positive integer l, let $K^l$ be the l-th principal congruence subgroup of G(O). A continuous irreducible representation of G(O) is called regular of level l if it is trivial on $K^{l+1}$ and its restriction to $K^l/K^{l+1} \\simeq \\mathfrak{g}(k)$ consists of characters with G(k)-stabiliser of minimal dimension. 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