We study -types of degenerate principal series of by using two realizations of these infinite-dimensional representations. The first model we use is the classical compact picture; the second model is conjugate to the noncompact picture via an appropriate partial Fourier transform. In the first case, we find a family of -finite vectors that can be expressed as solutions of specific hypergeometric differential equations; the second case leads to a family of -finite vectors whose expressions involve Bessel functions.
"Special functions associated with -types of degenerate principal series of ." Kyoto J. Math. 60 (4) 1373 - 1398, December 2020. https://doi.org/10.1215/21562261-2019-0065