Some remarks on degenerate principal series (Q1127906)

Let \(G\) be a split connected reductive Lie group (resp. \(p\)-adic group), \(P=MU\) a standard parabolic subgroup. This paper gives a criterion for the irreducibility of \(\text{Ind}_P^G (\rho\otimes 1)\) when \(\rho\) is an irreducible representation of \(M\) whose Langlands data comes from the minimal parabolic subgroup of \(M\). This criterion is then applied to examples of degenerate principal series (i.e., \(\rho\) one-dimensional).