A proof of Casselman-Shahidi's conjecture for quasi-split classical groups (Q2764788)

The author proves Casselman-Shahidi's conjecture on the irreducibility of standard modules for classical \(p\)-adic groups [Ann. Sci. Éc. Norm. Supér., IV. Sér. 31, No. 4, 561-589 (1998; Zbl 0947.11022)]. NEWLINENEWLINENEWLINEA standard module, denoted by \(I(\nu, \pi)\), is the representation unitarily induced from \(\pi\) and \(\nu\), where \(\pi\) is an irreducible tempered representation and \(\nu\) is in the positive Weyl chamber. Let \(J(\nu, \pi)\) be the unique Langlands quotient of \(I(\nu, \pi)\). The main result is the following: The standard module \(I(\nu, \pi)\) is irreducible if and only if the Langlands quotient \(J(\nu, \pi)\) is generic.