Given a unitary representation T of a finite group G in C, write M for the variety of such representations which are unitary equivalent to T . The representation T is said to be frequent if the dimension of the variety M is maximal (among all representations of G in the same complex space). We prove that the irreducible representations are distributed, in the frequent representation (of large d...

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...

is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...

Given a unitary representation U of a locally compact abelian group G, we investigate the relationship between two cocycles a,, a2: Vax = a2+ b for some unitary operator V commuting with U and some coboundary b. A necessary and sufficient condition is given in terms of canonical-finite measures defined on G 1. These results are applied to the representation of Z defined by the shift of a statio...

Given a discrete group and a unitary representation on a Hilbert space H, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of H. As a consequence, combining this result with known frame theory, we can recover in a simple way all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation.

Let g be a complex reductive Lie algebra. We investigate a formalism for producing a natural model for representations of sl(2) × g which decompose in such a way so as to produce interesting correspondences between representations of sl(2) and of g. Our formalism generalizes the standard dual pair SL(2)× O(2n). We use it to obtain a formally unitary representation of sl(2,R)×u(3) that essential...

Empirical evidence from both utility and psychophysical experiments suggests that people respond quite differently—perhaps discontinuously—to stimulus pairs when one consequence or signal is set to ‘zero.’ Such stimuli are called unitary. The author’s earlier theories assumed otherwise. In particular, the key property of segregation relating gambles and joint receipts (or presentations) involve...

1. In the mathematical theory of fields of elementary particles one has to do with a representation of the unitary group on a Hilbert space 77. With any such representation T and subspace M of 77 there is associated a self-adjoint operator called the "number of particles in M." The particle interpretation of general wave fields is made possible in the first instance by the fact that these opera...