Recently, in a joint work with Alberto Minguez, we dealt with the class of representations of p-adic GL_n that appear as quotients of standard representations. This approach gives an intrinsic proof to a long-sought irreducibility criterion for parabolic induction, while the techniques were inspired by recent work of Hernandez on representations of quantum affine algebras.
In this partly educational talk, I would like to discuss the methods of our proof and its applications, in addition to the relations between the p-adic and the quantum affine setting. We will see how various notions manifest themselves across the categorical equivalences, such as the classical Langlands Quotient Theorem that becomes a parallel of the highest weight theory.
This is the last talk of our workgroup on Intertwining operators and R-matrices