In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere Sn ≃ SO(n + 1)/SO(n) and the spherical functions of the n-dimensional real projective space P n(R) ≃ SO(n + ...

For any reduced crystallographic root system, we introduce a unitary representation of the (extended) affine Hecke algebra given by discrete difference-reflection operators acting in a Hilbert space of complex functions ...

In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R ...

We introduce an explicit representation of the double affine Hecke algebra (of type A(1)) at q = 1 that gives rise to a periodic counterpart of a well-known Fourier transform associated with the affine Hecke algebra. (C) ...

In this article, using the notion of group contraction, we obtain the spherical functions of the strong Gelfand pair (M(n),SO(n)) as an appropriate limit of spherical functions of the strong Gelfand pair (SO(n+1),SO(n)) ...

The tensorial spin-s and the spin weighted spherical harmonics are functions on the sphere which are extremely useful for many calculations in general relativity. These sets of functions constitute two orthonormal bases ...

In this paper, we determine all irreducible spherical functions of any K-type associated to the pair (G;K) = (SO(4); SO(3)). This is accomplished by associating to a vector valued function H = H(u) of a real variable ...

We present an approach to sums of random Hermitian matrices via the theory of spher- ical functions for the Gelfand pair (U(n) Herm(n), U(n)). It is inspired by a similar approach of Kieburg and Kösters for products of ...

In this paper, we describe the irreducible spherical functions of fundamental K-types associated with the pair (G, K) = (SO(n + 1), SO(n)) in terms of matrix hypergeometric functions. The output of this description is that ...