Helgason-Schiman Formula for Semisimple Lie Groups of Arbitrary Rank
- *Corresponding Author:
- Bassey UN
Department of Mathematics
University of Ibadan, Ibadan, Nigeria
E-mail: [email protected]
Received date: July 21, 2014; Accepted date: November 29, 2014; Published date: December 05, 2014
Citation: Bassey UN, Oyadare OO (2015) Helgason-Schiman Formula for Semisimple Lie Groups of Arbitrary Rank. J Generalized Lie Theory Appl 9:216. doi:10.4172/1736-4337.1000216
Copyright: © 2015 Bassey UN, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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 -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.