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We consider R3 as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary τ∈ SO(3) ^ , let Eτ be the homogeneous vector bundle over R3 associated with τ. An interesting problem consists in studying the set of bounded linear operators over the sections of Eτ that are invariant under the action of SO(3) ⋉ R3. Such operators are in correspondence with the End(Vτ) -valued, bi-τ-equivariant, integrable functions on R3 and they form a commutative algebra with the convolution product. We develop the spherical analysis on that algebra, explicitly computing the τ-spherical functions. We first present a set of generators of the algebra of SO(3) ⋉ R3-invariant differential operators non Eτ. We also give an explicit form for the τ-spherical Fourier transform, we deduce an inversion formula and we use it to give a characterization of End(Vτ) -valued, bi-τ-equivariant, functions on R3. Fil: Díaz Martín, Rocío Patricia. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina Fil: Levstein, Fernando. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina

The multiplicity-free subgroups (strong Gelfand subgroups) of wreath products are investigated. Various useful reduction arguments are presented. In particular, we show that for every finite group [Formula: see text], the wreath product [Formula: see text], where [Formula: see text] is a Young subgroup, is multiplicity-free if and only if [Formula: see text] is a partition with at most two parts, the second part being 0, 1, or 2. Furthermore, we classify all multiplicity-free subgroups of hyperoctahedral groups. Along the way, we derive various decomposition formulas for the induced representations from some special subgroups of hyperoctahedral groups.