ABSTRACT:
Dual reductive pairs are important algebraic objects in
representation theory of p-adic groups.
These were studied by Roger Howe for the symplectic group, and through the
Weil representation of the symplectic group, play an important role in the
subject.
In this lecture, we classify dual reductive pairs in all excetional Lie
groups. As a step in this
direction, we also discuss classification of exceptional Lie groups over
general fields in terms of Octonion and Jordan algebras, and then use
Hasse principle for Galois cohomology to classify them over number fields.
