Non-highest weight representations of the current algebra so(1, n), and Laplace Operators. Abstract We constructed canonical non-highest weight unitary irreducible representation of so(1, n) current algebra as well as canonical non-highest weight non-unitary representations, We constructed certain Laplacian operators as elements of the universal enveloping algebra, acting in representation spac...

We do a study of the real representations of the Poincare group, motivated by the following: i) the classical electromagnetic field —from which the Poincare group was originally defined— transforms as a real representation of the Poincare group; ii) the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity...

By further sharpening the Helgason-Johnson bound in 1969, this paper classifies all irreducible unitary representations with non-zero Dirac cohomology of Hermitian symmetric real form E7(−25).

We give a classification of irreducible metabelian representations from a knot group into SL(n,C) and GL(n,C). If the homology of the n–fold branched cover of the knot is finite, we show that every irreducible metabelian SL(n,C) representation is conjugate to a unitary representation and that the set of conjugacy classes of such representations is finite. In that case, we give a formula for thi...

We use the group-theoretic interpretation of the AdS/CFT correspondence which we proposed earlier in order to lift intertwining operators acting between boundary conformal representations to intertwining operators acting between bulk conformal representations. Further, we present the classification of the positive energy (lowest weight) unitary irreducible representations of the D = 6 superconf...

A theorem of Glimm states that representation theory of an NGCR C∗-algebra is always intractable, and the Cuntz algebra ON is a case in point. The equivalence classes of irreducible representations under unitary equivalence cannot be captured with a Borel cross section. Nonetheless, we prove here that wavelet representations correspond to equivalence classes of irreducible representations of ON...

We provide a detailed analysis of atomic ∗-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a direct sum or direct integral of irreducible atomic representations. The building blocks are described as the minimal ∗-dilations of defect free representations modelled on finite groups of rank 2.

All representations of finite groups and compact linear groups can be expressed as unitary matrices given an appropriate choice of basis. This makes them natural candidates for implementation using quantum circuits. As shown here, the irreducible representations of the symmetric group Sn, the alternating group An, the unitary groups U(n) and SU(n), and the special orthogonal group SO(n) can eac...

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is...