Systems of imprimitivity for wreath products

Knapsack Problems for Wreath Products

In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under...

Zonal polynomials for wreath products

The pair of groups, symmetric group S2n and hyperoctohedral group Hn , form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions of (S2n, Hn) into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials. A wreath product generalization of the Gelfand pair (S2n, ...

Compression bounds for wreath products

We show that if G and H are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath G ≀ H . We also prove an analogous result for coarse embeddings of wreath products. In the special case G = Z, H = Z ≀ Z our result implies that the Hilbert compression exponent of Z ≀ (Z ≀ Z) is at least 1/4, answering a question posed ...

Wreath products for edge detection

Wreath product group based spectral analysis has led to the development of the wreath product transform, a new multiresolution transform closely related to the wavelet transform. In this work, we derive the lter bank implementation of a simple wreath product transform and show that it is in fact, a multiresolution Roberts Cross edge detector. We also derive the relationship between this transfo...

The Wreath Products