Symplectic groupoids were introduced in the 1980’s by Weinstein
and Karasev to study quantization of Poisson manifolds, and have
been extensively studied ever since. However, few explicit constructions
and examples are known. In this talk, we will show that symplectic
leaves in standard semisimple Poisson Lie groups are naturally
symplectic groupoids or modules thereof, thus providing the
literature with a large family of examples of symplectic groupoids.
I will explain how the symplectic groupoid structure on these symplectic
leaves is a consequence of a general construction of action Poisson
groupoids associated to actions of pairs of Lie bialgebras.
This is joint work with J.-H. Lu.