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.
Citation
UN Bassey. OO Oyadare. "Helgason-Schiman Formula for Semisimple Lie Groups of Arbitrary Rank." J. Gen. Lie Theory Appl. 9 (1) 1 - 6, 2015. https://doi.org/10.4172/1736-4337.1000216
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