Spherical harmonic analysis of affine buildings and Macdonald theory (B03)

• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 491392403

Spherical harmonic analysis is a key tool in the geometric analysis of Riemannian symmetric spaces. It admits various analogues and generalisations. In particular, there is a non-Archimedean version for affine buildings. One aspect of this project is the study of non-Archimedean Poisson transformations and their mapping properties. Moreover, we shall study spherical functions of Bruhat-Tits buildings and consider related open questions of harmonic analysis within the general framework of Macdonald theory, which considerably extends the geometric setting.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 358: Integral Structures in Geometry and Representation Theory
• Applicant Institution: Universität Bielefeld
• Project Heads: Professor Dr. Kai-Uwe Bux; Professor Dr. Joachim Hilgert; Professorin Dr. Margit Rösler