A Kazhdan-Lusztig theorem for quantum symmetric spaces (OZRSAB9)

In 2019, I made a conjecture, together with S. Neshveyev, L. Tuset and M. Yamashita, relating three different constructions of module C*-categories for the tensor C*-category of representations of a q- deformed semisimple compact Lie group, starting from the datum of a classical symmetric space of
compact type. This conjecture is still open at the moment, although some progress has been made (in the formal case). With this project, I want to allocate an intensive period of research to work on providing a resolution to this conjecture.

Keywords:Tensor C*-categories, Deformation quantization, Higher representation theory

Disciplines:Category theory, homological algebra, Group theory and generalisations, Topological groups, Lie groups, Abstract harmonic analysis, Functional analysis