Search results for "Trivial representation"

Modular representation theory and pi-algebras

1988

(1988). Modular representation theory and pi-algebras. Communications in Algebra: Vol. 16, No. 10, pp. 2043-2067.

Elements of General Representation Theory

1982

In Chapter V, classical representation theory was studied. This is the theory of the group-ring KG and the KG-modules, where K is an algebraically closed field of characteristic 0. (Many theorems remain valid under the hypothesis that K is algebraically closed and that char K does not divide the order of G). In this case, KG is semisimple and all KG-modules are completely reducible. For many purposes it is therefore sufficient to handle the irreducible representations.

The cauchy problem for non-linear Klein-Gordon equations

1993

We consider in ℝ n+1,n≧2, the non-linear Klein-Gordon equation. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the …

A remark on conjectures in modular representation theory

1987

Character problems in classical representation theory

1987

New solutions of the hamiltonian and diffeomorphism constraints of quantum gravity from a highest weight loop representation

1991

Abstract We introduce a highest weight type representation of the Rovelli-Smolin algebra of loop observables for quantum gravity. In terms of this representation, new solutions of the hamiltonian and diffeomorphism constraints are given. Assuming the locality of the quantum hamiltonian constraint we show that any functional depending on the generalized link class of the disjoint union of arbitrary simple loops is a solution. Finally we argue that this is the general solution in the irreducible representation space.

On the representation theory of quantum Heisenberg group and algebra

1994

We show that the quantum Heisenberg groupH q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU q (h(1)). We derive left and right regular representations forU q (h(1)) as acting on its dualH q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. By duality, left and right regular representations for quantum Heisenberg group with the quantum Heis…