Degenerate principal series representations, obtained by parabolic induction from characters on Levi components of maximal parabolic subgroups, play a pivotal role in harmonic analysis and representation theory. The intricate structure of these representations, particularly their sub quotients and K-types, has been extensively studied. They are also intimately connected with theta correspondence in the sense that theta lifts of trivial representations can be embedded into them.  

In this talk, I will introduce the basic concepts of degenerate principal series and their applications.