Special functions associated withK-types of degenerate principal series of Sp(n,C)

摘要

We study K-types of degenerate principal series of Sp(n,C) 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 K-finite vectors that can be expressed as solutions of specific hypergeometric differential equations; the second case leads to a family of K-finite vectors whose expressions involve Bessel functions.