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## Banach Center Publications

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## Spherical functions on spheres of rank two

### Volume 113 / 2017

Banach Center Publications 113 (2017), 395-408 MSC: Primary 43A90; Secondary 42C05. DOI: 10.4064/bc113-0-19

#### Abstract

Under a suitable multiplicity freeness assumption we show that the spherical functions of the pair $(\mathrm{SU}(n+1),\mathrm{SU}(n))$ can be described by families of vector-valued polynomials in two variables. The matrix weight that establishes the orthogonality is supported on the closed unit disc and depends on $n$. We calculate the matrix weight in a couple of examples using computer algebra.