For simplicity, call the Weil group of a local nonarchimedean field $F_v$ to be the following extension: $$1\longrightarrow F^\times_v\longrightarrow W_{F_v}\longrightarrow\text{Gal}(F_v/\mathbb Q_v)\longrightarrow 1.$$

Finding this definition to be lacking in terms of describing $\ell$-adic representations, Deligne modified it to what is known as the Weil-Deligne group, $WD_{F_v}=W_{F_v}\ltimes\mathbb G_a.$

Langlands in the Corvallis proceedings suggests that one should take instead $W'_{F_v}=W_{F_v}\times SL(2,\mathbb C)$.

Kottwitz (and Arthur, citing him) later writes that it is known that (the Langlands group) should be $L_{F_v}=W_{F_v}\times SU(2,\mathbb R)$, to give a natural bijection between the irreducible n-dimensional complex representations of $L_{F_v}$ irreducible admissible representations of $GL_n(F_v)$.

It seems that (3) is the accepted form of the Langlands group, is (2) then no longer relevant? Is (1) now subsumed under (3), so that one should really be thinking of the latter?

As a follow up question, why is it that $L_F$ *should be* an extension of $W_F$ by a compact group (Kottwitz)? Or even a reductive, proalgebraic group (Langlands)?