The Generalized Injectivity Conjecture

The Generalized Injectivity Conjecture of Casselman-Shahidi states that the unique irreducible
generic subquotient of a (generic) standard module is necessarily a subrepresentation. It is related
to $L$-functions, as studied by Shahidi, hence has some number-theoretical flavor, although our technics lie
in the fields of representations of reductive groups over local fields.

It was proven for classical groups (SO(2n+1), $Sp_{2n}$, SO(2n)) by M.Hanzer in 2010.
In this talk, I will first explain our interest in this conjecture, and describe its main ingredients.
I will further present our proof (under some restrictions) which uses techniques more amenable
to prove this conjecture for all quasi-split groups.