Related papers: The Poincar\'e half-plane for informationally comp…
We present a new method to construct integration-by-part (IBP) identities from the viewpoint of differential geometry. Vectors for generating IBP identities are reformulated as differential forms, via Poincar\'{e} duality. Using the tools…
A method of Proctor [European J. Combin. 5 (1984), no. 4, 331-350] realizes the set of arbitrary plane partitions in a box and the set of symmetric plane partitions as bases of linear representations of Lie groups. We extend this method by…
The simplices and the complexes arsing form the grading of the fundamental (desymmetrized) domain of arithmetical groups and non-arithmetical groups, as well as their extended (symmetrized) ones are described also for oriented manifolds in…
We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincar\'e polynomial. We prove a Terao-type factorization statement on the splitting of…
We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by…
The representations of the Schr\"odinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable…
Every (full) finite Gabor system generated by a unit-norm vector $g\in \mathbb{C}^d$ is a finite unit-norm tight frame (FUNTF), and can thus be associated with a (Gabor) positive operator valued measure (POVM). Such a POVM is…
We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\G$ of $SL(2, \bR)$…
We propose a scheme that can realize a class of positive-operator-valued measures (POVMs) by performing a sequence of projective measurements on the original system, in the sense that for an arbitrary input state the probability…
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…
We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and…
We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark's theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to…
Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge…
The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.
A method to construct integrable deformations of Hamiltonian systems of ODEs endowed with Lie-Poisson symmetries is proposed by considering Poisson-Lie groups as deformations of Lie-Poisson (co)algebras. Moreover, the underlying Lie-Poisson…
Poincar\'e profiles are a family of analytically defined coarse invariants, which can be used as obstructions to the existence of coarse embeddings between metric spaces. In this paper we calculate the Poincar\'e profiles of all connected…
An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum…
In previous papers we extended the Lorentz and Poincare groups to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The groups are…
In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for P\"oschl-Teller potentials. These states are built from a…
We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian…