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classes of irreducible admissible representations of GL_n(K) and certain n-dimensional representations of the Weil-Deligne group of K.

The Weil-Deligne group often shows up through its representations. In such cases, the Weil-Deligne group is sometimes taken to be W_K × SL(2,C) or W_K × SU(2,R), or is simply done away with and Weil-Deligne representations of W_K are used instead.

In the archimedean case,

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