Related papers: On the center of two-parameter (v,t)-quantum group…
Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy…
We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient…
This volume contains a mildly expanded version of lectures and talks at seminars and conferences, as well as review papers on subjects listed in the title of the volume. A great deal of these texts have already been published or sent to…
The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well…
We give the exact contributions of Harish-Chandra transform, $(\mathcal{H}f)(\lambda),$ of Schwartz functions $f$ to the harmonic analysis of spherical convolutions and the corresponding $L^{p}-$ Schwartz algebras on a connected semisimple…
The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds is well known. We bring this solution into a TQFT-like form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is…
Essential elements of quantum theory are derived from an epistemic point of view, i.e., the viewpoint that thetheory has to do with what can be said about nature. This gives a relationship to statistical reasoning and to other areas of…
We investigate the group structure of center-preserving automorphisms of the finite Heisenberg group over $\mathbb Z_N$ with $U(1)$ extension, which arises in finite-dimensional quantum mechanics on a discrete phase space. Constructing an…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
In this paper is presented an abstract theory of quantum processors and controllers, special kind of quantum computational network defined on a composite quantum system with two parts: the controlling and controlled subsystems. Such…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
After a brief introduction to the Attractor Mechanism, we review the appearance of groups of type E7 as generalized electric-magnetic duality symmetries in locally supersymmetric theories of gravity, with particular emphasis on the…
We show the connection between the extended center of the quantum group in roots of unity and the restriction of the $XXZ$ model. We also give explicit expressions for operators that respect the restriction and act on the state space of the…
The aim of this paper is to suggest a new interpretation of quantum indeterminacy using the notion of polar duality from convex geometry. Our approach does not involve the usual variances and covariances, whose use to describe quantum…
We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions…
A {\it Schmidt group} is a non-nilpotent finite group in which each proper subgroup is nilpotent. Each Schmidt group G can be described by three parameters p, q and v, where p and q are different primes and v is a natural number, $v\ge 1$.…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
We consider isomorphisms and automorphisms of quantum groups. Let $k$ be a field and suppose $p, q\in k^*$ are not roots of unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_2)$ and $U_p(\mathfrak{sl}_2)$ over a field $k$ are…
We discuss three applications of efficient quantum algorithms to determining properties of permutations and group automorphisms. The first uses the Bernstein-Vazirani algorithm to determine an unknown homomorphism from $Z_{p-1}^{m}$ to…
We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.