Summary:

The focus of Project B3 is spherical harmonic analysis on affine buildings. This theory exhibits striking analogies with the corresponding Archimedean theory for Riemannian symmetric spaces. We shall study equivariant Poisson transformations and their inverse boundary value maps as well as positive definite spherical functions. Here, group representations play a crucial role. We shall also consider generalisations in the context of Macdonald--Cherednik theory, where the role of the symmetric space is replaced by an affine Hecke algebra. Furthermore, we will consider open questions in harmonic analysis related to associated families of Macdonald polynomials, such as the existence of positivity-preserving dual convolution structures.

Recent preprints:

24032 Thomas Baier, Ana Cristina Ferreira, Joachim Hilgert, José M. Mourão, João P. Nunes | |

Fibering polarizations and Mabuchi rays on symmetric spaces of compact type | |

Projects: B3, B4 |

24031 Ian Leary, Jason Semeraro | |

Spectra of subrings of cohomology generated by characteristic classes for fusion systems | |

Project: B3 |

24003 Dominik Brennecken, Margit Rösler | |

Limits of Bessel functions for root systems as the rank tends to infinity | |

Project: B3 |