RVP lecture: Langlands' functoriality viewed as a kind of function theoretic Poisson formula problem
Seminar Room 1, Newton Institute
Langlands' functoriality conjecture is one of the most important problems in automorphic representations theory.
In the case of transfer of unramified representations between linear groups, we give an equivalent formulation of this conjecture which looks like a Poisson formula :
two linear functionnals defined on some huge space of functions on adelic groups have to be equal.
These two liear functionnals are defined by some local constructions (on groups over the local completions of the global field) followed by summation over some groups of rational points.