We study a second example of the phenomenon studied in the article “The complex Lorentzian Leech lattice and the bimonster”. We find 14 roots 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 the reflections in these 14 roots generate the automorphism group of L. The ...

Weyl points and line nodes are three-dimensional linear point and line degeneracies between two bands. In contrast to two-dimensional Dirac points, which are their lower-dimensional analogues, Weyl points are stable in momentum space, and the associated surface states are predicted to be topologically non-trivial. However, Weyl points are yet to be discovered in nature. Here, we report photonic...

Approximately fifty percent of Weyl’s theorem fails to transfer from Hilbert space operators to their tensor product. As a biproduct we find that the product of circles in the complex plane is a limaçon. 0. Introduction To say that “Weyl’s theorem holds”, for a bounded operator T ∈ B(X) on a Banach space X , is to assert [2],[4],[5] that 0.1 σ(T ) \ ωess(T ) = π 00 (T ) ≡ iso σ(T )∩π 0 (T ) : t...

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

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...