Wednesday 17 June 2026, 16:00 - 17:00 in HG00.086
Philip Schloesser (Radboud)
Radial Parts for Pseudo-Riemannian Symmetric Pairs
Matrix spherical functions of symmetric pairs (G,H) are a fruitful source of special functions. One usually studies their restrictions to an appropriate torus. These diagonalise a commutative algebra of differential operators that arises from invariant differential operators on G via the radial part decomposition. I first recap the established theory for Riemannian symmetric pairs (by Cartan, Harish-Chandra, and others) and then sketch some of the obstacles that the pseudo-Riemannian case presents. These obstacles are addressed by a decomposition by Matsuki, which I use to construct a radial part decomposition for the pseudo-Riemannian case.