Intertwining operators and geometry

BGG complex and Poisson transforms as ingredients for a proof of the Baum-Connes conjecture with coefficients for real rank one Lie groups

20 janv. 2025, 16:30

50m

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Pierre Julg (Université d'Orléans)

Description

We describe the construction of a Fredholm module adapted to the proof of the Baum-Connes (or Connes-Kasparov) conjecture with coefficients for real rank one simple Lie groups (e.g. $Sp(n,1)$). The main ingredients are a BGG complex on the flag manifold associated to the Borel subgroup, and a suitable Poisson transform from the above complex to the space of L2-harmonic forms on the associated symmetric space.