On one-dimensional two-way infinite quantum lattice system, a property of translationally invariant stationary states with nonvanishing current expectation is investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show that spectrum of the unitary operators, energy-momentum spectrum with respect to the ...

Using a new definition of rank for representations of semisimple groups, sharp results are proved for the decay of matrix coefficients of unitary representations of two types of non-split p-adic simple algebraic groups of exceptional type. These sharp bounds are achieved by minimal representations. It is also shown that in one of the cases considered, the minimal representation is isolated in t...

Following hep-th/0305177, we write the boundary state of half S-brane in bosonic string theory as a grand canonical partition function of a unitary matrix model. From this representation, it follows that the annulus amplitude can be written as a grand canonical partition function of a unitary two-matrix model. We also show that the contribution of the exponentially growing couplings to the time...

On one-dimensional two-way infinite lattice system, a property of stationary (space-) translationally invariant states with nonvanishing current expectations are investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show, by applying Goldstone-theoremlike argument, that spectrum of the unitary operator...

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This report describes an approach for representation of quantum operators through rotations and rotation through quantum operators. The approach of the proposed method transforms rotation in a kind of a unitary matrix that corresponds to the rotation. Operations with qubits are very similar to the rotation, but with an added phase coefficient. This fact is used to create a process for rotation ...

If G is any finite product of orthogonal, unitary and symplectic matrix groups, then Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group G. If G is orthogonal, unitary or symplectic, then Wilson loops associated to the natural representation of G are enough. This extends a result of A. Sengupta [7]. In partic...

Abstract The aim of the paper is to create a link between theory reproducing kernel Hilbert spaces (RKHS) and notion unitary representation group or groupoid. More specifically, it demonstrated on one hand how construct positive definite an RKHS for given group(oid), other retrieve groupoid from defined that group(oid) with help Moore–Aronszajn theorem. constructed inspired by in terms convolut...

To understand nonabelian Fourier analysis, we first need to introduce some notions from group representation theory. For further information on this subject, a good basic reference is the book Linear Representations of Finite Groups by Serre. A linear representation (or simply representation) of a group G over the vector space Cn is a homomorphism σ : G → GL(Cn), i.e., a map from group elements...