Search results for "Group representation"

Initial Data for Non-Linear Evolution Equations and Differentiable Vectors of Group Representations

1995

Regularity properties of non-linear Lie algebra representations are defined. These properties are satisfied in examples given by evolution equations. We prove that this regularity implies that the set of C ∞ vectors for the non-linear group representation obtained by integration of the Lie algebra representation coincide with the set of C ∞ vectors of the linear part (the order one term) of this group representation.

The McKay conjecture and Galois automorphisms

2004

The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the ?McKay conjecture? which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.

Séparation des orbites coadjointes d'un groupe exponentiel par leur enveloppe convexe

2008

Resume Revenant sur la question de la separation des representations unitaires irreductibles d'un groupe de Lie exponentiel G par leur application moment, nous presentons ici une nouvelle solution : au lieu de prolonger l'application moment a l'algebre enveloppante de G , nous proposons de definir une application (non lineaire) Φ de g ∗ dans le dual g + ∗ de l'algebre de Lie d'un groupe resoluble G + , de prolonger les representations de G a G + de telle facon que les orbites coadjointes correspondantes de G + soient caracterisees par l'adherence de leur enveloppe convexe. Ceci nous permet de separer les representations irreductibles de G .

Symmetric (79, 27, 9)-designs Admitting a Faithful Action of a Frobenius Group of Order 39

1997

AbstractIn this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a non-abelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1320 non-isomorphic designs. The orders of the full automorphism groups of these designs all divide 8 · 3 · 13.

On the classification of topological 4-manifolds with finite fundamental group

1988

Formal Group Laws for Affine Kac-Moody groups and group quantization

1987

We describe a method for obtaining Formal Group Laws from the structure constants of Affine Kac-Moody groups and then apply a group manifold quantization procedure which permits construction of physical representations by using only canonical structures on the group. As an intermediate step we get an explicit expression for two-cocycles on Loop Groups. The programme is applied to the AffineSU(2) group.

Chiral Symmetry of Baryons

2001

We study chiral symmetry aspects of the positive and negative parity baryons by identifying them with linear representations of the chiral group $SU(N_{f}) \otimes SU(N_{f})$. It is shown that there are two distinctive schemes: naive and mirror assignments. We construct linear sigma models for baryons in the two assignments and examine their physical implications. Then we investigate properties of the naive and mirror nucleons microscopically by using QCD interpolating fields. Finally, we propose experiments to distinguish the two chiral assignments for the nucleon.

A simple proof for the formula to get symmetrized powers of group representations

1993

A general formula to decompose the p-power of irreducible representations of an arbitrary space group into sum of sets of irreducible representations of such a group, having identical permutational symmetry, is presented. Its proof is based upon a straightforward application of the properties of the generalized projection (shift) operators. © 1993 John Wiley & Sons, Inc.

Quantization on the Virasoro group

1990

The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc≦1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace ℋ(c, h), the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. ℋ(c, h) is a proper subspace of the sp…

Separation of representations with quadratic overgroups

2011

AbstractAny unitary irreducible representation π of a Lie group G defines a moment set Iπ, subset of the dual g⁎ of the Lie algebra of G. Unfortunately, Iπ does not characterize π. If G is exponential, there exists an overgroup G+ of G, built using real-analytic functions on g⁎, and extensions π+ of any generic representation π to G+ such that Iπ+ characterizes π.In this paper, we prove that, for many different classes of group G, G admits a quadratic overgroup: such an overgroup is built with the only use of linear and quadratic functions.