Contents 1. Introduction 1 2. The usual Weyl case 2 3. The affine Weyl quantization 3 4. Affine Husimi 5 5. The result 6 6. Possible generalizations 8 Appendix A. The Mellin transform 8 References 8 Abstract. We study a generalization of Husimi function in the context of wavelets. This leads to a nonnegative density on phase-space for which we compute the evolution equation corresponding to a S...

Construction of an infinite dimensional differentiable manifold R∞ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra (P ∗ p M [[~]], ◦) and a Weyl algebra bundle (P∗M[[~]], ◦) are presented. Continuity of the ◦-product in the Tichonov topology is proved. Construction of the ∗-product of the Fedosov type in terms of theory of connectio...

We prove a version of Schur–Weyl duality over finite fields. We prove that for any field k, if k has more than r elements, then Schur– Weyl duality holds for the rth tensor power of a finite dimensional vector space V . Moreover, if dimV is at least r + 1 then the natural map kSr → EndGL(V )(V ) is an isomorphism; this isomorphism may fail if dimk(V ) is not strictly larger than r.

A Banach space operator T ∈ B(X ) is polaroid if points λ ∈ isoσσ(T ) are poles of the resolvent of T . Let σa(T ), σw(T ), σaw(T ), σSF+(T ) and σSF−(T ) denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower semi–Fredholm spectrum of T . For A, B and C ∈ B(X ), let MC denote the operator matrix (

Conformal Weyl and Cotton tensors are dimensionally reduced by a Kaluza– Klein procedure. Explicit formulas are given for reducing from four and three dimensions to three and two dimensions, respectively. When the higher dimensional conformal tensor vanishes because the space is conformallly flat, the lower-dimensional Kaluza–Klein functions satisfy equations that coincide with the Einstein–Wey...

The BRST transformations for gravity with torsion including Weyl symmetry are discussed by using the so-called Maurer-Cartan horizontality conditions. Also the coupling of scalar matter fields to gravity is incorporated in this analysis. With the help of an operator δ which allows to decompose the exterior space-time derivative as a BRST commutator we solve the Wess-Zumino consistency condition...

We study Weyl nodes in materials with broken inversion symmetry. We find based on first-principles calculations that trigonal Te and Se have multiple Weyl nodes near the Fermi level. The conduction bands have a spin splitting similar to the Rashba splitting around the H points, but unlike the Rashba splitting the spin directions are radial, forming a hedgehog spin texture around the H points, w...

We study a second example of the phenomenon studied in the article “The complex Lorentzian Leech lattice and the bimonster”. We find 14 reflections in the automorphism group of the the quaternionic Lorentzian Leech lattice L that form the Coxeter diagram given by the incidence graph of projective plane over F2. We prove that these 14 reflections generate the automorphism group of L. The investi...

The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl families of boundary relation...