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


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.


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UN Bassey. OO Oyadare. "Helgason-Schiman Formula for Semisimple Lie Groups of Arbitrary Rank." J. Gen. Lie Theory Appl. 9 (1) 1 - 6, 2015.


Published: 2015
First available in Project Euclid: 30 September 2015

zbMATH: 06499575
MathSciNet: MR3624038
Digital Object Identifier: 10.4172/1736-4337.1000216

Keywords: H−function , Helgason-Schiffman formula , Semi simple Lie group , Spherical functions

Rights: Copyright © 2015 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.9 • No. 1 • 2015
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