Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space

Details Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space

2002-03-20

arxiv.org/abs/math/0203211v1

Mathematics

Representation Theory

55 pages

Scientific paper

The main purpose of this paper is to compute all irreducible spherical functions on $G={SL}(2,{\mathbb C})$ of arbitrary type $\delta\in \hat K$, where $K={SU}(2)$. This is accomplished by associating to a spherical function $\Phi$ on $G$ a matrix valued function $H$ on the three dimensional hyperbolic space ${\mathbb H}=G/K$. The entries of $H$ are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of $H$ in terms of Gauss' functions ${}_2F_1$. Just as in the compact instance treated in [GPT] there is a useful role for a special class of generalized hypergeometric functions ${}_{p+1}F_p$.

Affiliated with

Also associated with

No associations

Rating

Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-495242