Spherical Harmonics on the Heisenberg Group

Combinatorics and Spherical Functions on the Heisenberg Group

Let V be a finite dimensional Hermitian vector space and K be a compact Lie subgroup of U(V ) for which the representation of K on C[V ] is multiplicity free. One obtains a canonical basis {pα} for the space C[VR] of K-invariant polynomials on VR and also a basis {qα} via orthogonalization of the pα’s. The polynomial pα yields the homogeneous component of highest degree in qα. The coefficients ...

Spherical Harmonics

5 Spherical Harmonics 7 5.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.1 Harmonic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

On a spherical code in the space of spherical harmonics

In this short note we propose a new method for construction new nice arrangement on the sphere Sd using the spaces of spherical harmonic.

Spherical Functions for the Action of a Finite Unitary Group on a Finite Heisenberg Group

The action of the unitary group on the real Heisenberg group yields a Gelfand pair. The associated spherical functions are well known and have been computed independently by many authors. In this paper we develop a discrete counterpart to this story by replacing the real numbers by a finite field of odd characteristic. This produces a finite Gelfand pair whose spherical functions are computed e...

3 Generalized Spherical Harmonics