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# Weil group, Weil-DelingeWeil-Deligne group scheme and conjectural Langlands group

I was reading a series of article from the Corvallis volume. There are couple of questions which came to my mind:

1. Why do we need to consider representation of Weil-Delinge Weil-Deligne group? That is what is an example of irreducible admissible representation of $Gl(n,F)$ which does not correspond to a representation of $W_F$ of dimension $n$ ? An example for $n=2$ will be of great help.

2. In the setting of global Langlands conjecture, why extension of $W_F$ by $G_a$ or products of $W'_{F_v}$ does not work?

Thank you.

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# Weil group, Weil-Delinge group scheme and conjectural Langlands group

I was reading a series of article from the Corvallis volume. There are couple of questions which came to my mind:

1. Why do we need to consider representation of Weil-Delinge group? That is what is an example of irreducible admissible representation of $Gl(n,F)$ which does not correspond to a representation of $W_F$ of dimension $n$ ? An example for $n=2$ will be of great help.

2. In the setting of global Langlands conjecture, why extension of $W_F$ by $G_a$ or products of $W'_{F_v}$ does not work?

Thank you.