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This work examines the argument of weak values for general observables and develops a geometric description on the Bloch sphere. We apply the Majorana symmetric representation to reach this goal. The weak value of a general observable is…
We develop the theory of projective endofunctors for modules of Khovanov algebras $K$ of type B. In particular we compute the composition factors and the graded layers of the image of a simple module under such a projective functor. We then…
We give explicit transforms for Hilbert spaces associated with positive definite functions on $\mathbb{R}$, and positive definite tempered distributions, incl., generalizations to non-abelian locally compact groups. Applications to the…
Manifestly covariant formulation of discrete-spin, real-mass unitary representations of the Poincar\'e group is given. We begin with a field of spin-frames associated with 4-mometa p and use them to simplify the eigenvalue problem for the…
For a local field $F$ and an Artinian local coefficient ring $\Lambda$ with the same positive residue characteristic $p$ we define, for any $e\in{\mathbb N}$, a category ${\mathfrak C}^{(e)}(\Lambda)$ of ${\rm GL}_2(F)$-equivariant…
A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…
Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
We extend some results of group representation theory and von Neumann algebras to the quaternionic Hilbert space case, proving the double commutant theorem (whose quaternionic proof requires a different procedure) and extend to the…
We consider converses to the density theorem for irreducible, projective, unitary group representations restricted to lattices using the dimension theory of Hilbert modules over twisted group von Neumann algebras. We show that under the…
The vector valued theta series of a positive-definite even lattice is a modular form for the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$. We show that the space of cusp forms for the Weil representation is generated by such…
The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given…
As a follow-up to work done in [7], some new insights to the structure of the socle of a semisimple Banach algebra is obtained. In particular, it is shown that the socle is isomorphic as an algebra to the direct sum of tensor products of…
In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…
The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner's little group) of the Poincar\'{e} group is re-examined in the massless…
Starting with conformally covariant correlation functions, a sequence of functional representations of the conformal algebra is constructed. A key step is the introduction of representations which involve an auxiliary functional. It is…
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated…
We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere,…
The Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the circle with the space of its adjoint…
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…