Source: Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 6 pages.
Abstract:
This paper extends the Helgason-Schiffman formula for the H-function on a
semisimple Lie group of real rank one to cover a semisimple Lie group G of
arbitrary real rank. A set of analytic $\mathbb{R}$ -valued cocycles are deduced
for certain real rank one subgroups of G. This allows a formula for the
c-function on G to be worked out as an integral of a product of their
resolutions on the summands in a direct-sum decomposition of the maximal abelian
subspace of the Lie algebra g of G. Results about the principal series of
representations of the real rank one subgroups are also obtained, among other
things.