Department Colloquium
Department of Mathematics
Princeton University
February 14th, 2001
The Principle of Functoriality and Classical Groups
The principle of functoriality is a far reaching, but quite precise,
conjecture of Langlands that relates
fundamental arithmetic information with equally
fundamental analytic information. The arithmetic information arises from the
solutions of algebraic equation. It includes data that classify algebraic
number fields, and more general algebraic varieties.
The analytic information arises
from spectra of differential equations and group representations.
It includes data that classify irreducible
representations of reductive groups.
We shall review the conjecture in elementary terms.
We shall then describe an important special
case that applies to representations of
classical matrix groups. The ultimate goal would
be to understand the representations of
these groups in terms of representations of general linear groups.