This paper shows how to reduce a Hamiltonian system on the cotangent bundle of a Lie group to a Hamiltonian system in the dual of the Lie algebra of a semidirect product. The procedure simplifies. unifies, and extends work of Greene, Guillemin, Holm, Holmes, Kupershmidt, Marsden, Morrison, Ratiu, Sternberg and others. The heavy top, compressible fluids, magnetohydrodynamics, elasticity, the Max...

For matroids M and N on disjoint sets S and T , a semidirect sum of M and N is any matroid K on S ∪ T that, like the direct sum and the free product, has the restrictionK|S equal toM and the contractionK/S equal toN . We abstract a matrix construction to get a general matroid construction: the matroid union of any rank-preserving extension ofM on the set S ∪ T with the direct sum ofN and the ra...

It is shown that two canonical maps arising in the Poisson bracket formulations of elasticity and superfluids are particular instances of general canonical maps between duals of semidirect product Lie algebras.

The wreath product W = A i T, where A ^ 1, is of type FP2 if and only if T is finite and A is of type FP2. 1991 Mathematics subject classification (Amer. Math. Soc): primary 20E22, 20F05, 20J05.

This paper continues the investigation in digital signal processing of spectral analysis on certain non-commutative nite groups|wreath product groups. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group based convolution is deened in both the spatial and spectral domain...

Let G be a finite group acting on the finite set X such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product G ∼ Sn on the generalized Boolean algebra BX(n). We explicitly block diagonalize the commutant of this action.

The theory of spectral analysis of a particular class of non-commutative groups|wreath products of cyclic groups| has been shown to have a group-based convolution that leads to a new class of noncommutative lters. These lters, with their group and scale-selective properties and their relationship to DFT lter banks, ooer some intriguing possibilities in signal processing applications. In this pa...

In 1997 Clarke, Han, and Zeng introduced a q-analogue of Euler’s difference table for n! using a key bijection Ψ on symmetric groups. In this paper we extend their results to the wreath product of a cyclic group with the symmetric group. By generalizing their bijection Ψ we prove the equidistribution of the triple statistics (fix, exc, fmaj) and (fix, exc, fmaf) on wreath products, where “fix”,...