Speaker: Sarah Dijols,
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), Sp2n, 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.