## Journal of Generalized Lie Theory and Applications

- J. Gen. Lie Theory Appl.
- Volume 9, Number 1 (2015), 6 pages.

### Helgason-Schiman Formula for Semisimple Lie Groups of Arbitrary Rank

UN Bassey and OO Oyadare

#### 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.

#### Article information

**Source**

J. Gen. Lie Theory Appl., Volume 9, Number 1 (2015), 6 pages.

**Dates**

First available in Project Euclid: 30 September 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jglta/1443617956

**Digital Object Identifier**

doi:10.4172/1736-4337.1000216

**Mathematical Reviews number (MathSciNet)**

MR3624038

**Zentralblatt MATH identifier**

06499575

**Keywords**

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

#### Citation

Bassey, UN; Oyadare, OO. Helgason-Schiman Formula for Semisimple Lie Groups of Arbitrary Rank. J. Gen. Lie Theory Appl. 9 (2015), no. 1, 6 pages. doi:10.4172/1736-4337.1000216. https://projecteuclid.org/euclid.jglta/1443617956