AbstractLet G be a reductive group over a local field F. The basic functions are certain spherical functions defined on G(F), whose Satake transform gives rise to the unramified L factors for an algebraic representation $\rho$ of the Langlands dual group ${^L}G$. They play important roles in the integral representation of global L functions. In general, the structure of such functions is not we...
AbstractLocally semisimple algebras (LS-algebras) are inductive limits of semisimple algebras, and can be fully characterized by their Bratteli diagrams ($\mathbb{N}$-graded graphs). (Finite) harmonic functions on Bratteli diagrams are a standard tool in the representation theory of LS-algebras and semifinite harmonic functions are a natural generalization. We plan to give an overview of the su...