There is no generally accepted way to define wavelets on permutations. We address this issue by introducing the notion of coset based multiresolution analysis (CMRA) on the symmetric group, find the corresponding wavelet functions, and describe a fast wavelet transform for sparse signals. We discuss potential applications in ranking, sparse approximation, and multi-object tracking.

We provide an algebraic classification of all supersymmetric domain wall solutions of maximal gauged supergravity in four and seven dimensions, in the presence of nontrivial scalar fields in the coset SL(8, IR)/SO(8) and SL(5, IR)/SO(5) respectively. These solutions satisfy first-order equations, which can be obtained using the method of Bogomol’nyi. From an eleven-dimensional point of view the...

The present paper deals with a maximal subgroup of the Thompson group, namely the group 2 + A9 := G. We compute its conjugacy classes using the coset analysis method, its inertia factor groups and Fischer matrices, which are required for the computations of the character table of G by means of Clifford-Fischer Theory. AMS subject classifications: 20C15, 20C40

If the fundamental quarks of QCD are replaced by massless adjoint quarks the pattern of the chiral symmetry breaking drastically changes compared to the standard one. It becomes SU(Nf ) →SO(Nf ). While for Nf = 2 the chiral Lagrangian describing the “pion” dynamics is well-known, this is not the case at Nf > 2. We outline a general strategy for deriving chiral Lagrangians for the coset spaces M...