Seminar

The local Langlands correspondence (conjecture) relates (infinite-dimensional) representations of p-adic reductive groups with (finite-dimensional) Galois representations. This can be viewed in many ways, and from the viewpoint of the representation theory, this gives us a "classification" of representations of p-adic reductive groups by viewing arithmetic objects as "simpler" parameters. Then it will be natural to study representation-theoretic problems in terms of arithmetic invariants. In this talk, we explain some cases which can be answered in this setup: the Gan-Gross-Prasad conjecture (a restriction problem) and formal degrees (a generalization of dimensions).