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1.
A. I. Shtern 《Russian Journal of Mathematical Physics》2012,19(4):499-501
We obtain simple necessary and sufficient conditions for the continuity of a locally bounded finite-dimensional representation of a connected locally compact group. We also prove that the discontinuity group of a locally bounded finite-dimensional representation of a connected locally compact group is a central subgroup in the closure of the image. 相似文献
2.
A. I. Shtern 《Russian Journal of Mathematical Physics》2009,16(4):566-567
In the paper, it is proved that a connected Lie group admits a (possibly discontinuous) faithful finite-dimensional representation
if and only if it admits a continuous faithful finite-dimensional representation, i.e., if and only if it is a linear Lie
group. 相似文献
3.
4.
A. I. Shtern 《Russian Journal of Mathematical Physics》2014,21(1):133-134
We continue the study of automatic continuity conditions for finite-dimensional representations of connected Lie groups. In particular, we claim that every locally bounded finite-dimensional representation of a connected Lie group is continuous on the commutator subgroup in the intrinsic Lie topology of the subgroup and continuous on the intersection of the commutator subgroup with the radical of the group in the original topology of the Lie group, thus correcting one of our previous results. 相似文献
5.
A. I. Shtern 《Russian Journal of Mathematical Physics》2006,13(4):458-465
An analog of the localization principle for the almost convergence for any element of the Fourier-Stieltjes algebra (Fourier-Stieltjes
transforms of bounded measures) is established for any unimodular amenable locally compact groups in neighborhoods of finite-dimensional
representations of these groups.
To the blessed memory of Yuri Solov’ev
Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting
the Leading Scientific Schools under grant no. NSh 619.203.1, and by the INTAS grant. 相似文献
6.
A. I. Shtern 《Russian Journal of Mathematical Physics》2008,15(4):552-553
The structure of norm continuous representations of locally compact groups in Banach spaces is specified.
Partially supported by the RFBR grant no. 08-01-00034 and by the Russian Government Program of Supporting Leading Scientific
Schools under grant no. NSh-1562.2008.1.
To the Memory of S. A. 相似文献
7.
8.
K. R. Parthasarathy 《Communications in Mathematical Physics》1969,15(4):305-328
We give here a systematic presentation of the theory of projective representations when antiunitary operators are present. In particular the imprimitivity theorem of Mackey is proved in this situation and all the unitary antiunitary representations of the extended Poincaré group are derived. 相似文献
9.
Unitary representations of some infinite dimensional groups 总被引:12,自引:2,他引:10
Graeme Segal 《Communications in Mathematical Physics》1981,80(3):301-342
We construct projective unitary representations of (a) Map(S
1;G), the group of smooth maps from the circle into a compact Lie groupG, and (b) the group of diffeomorphisms of the circle. We show that a class of representations of Map(S
1;T), whereT is a maximal torus ofG, can be extended to representations of Map(S
1;G), 相似文献
10.
Generalising known results [2] for vector groups, it is shown that, for an arbitrary multiplier ω for an arbitrary locally compact Abelian group G, there is a faithful normal semifinite trace on the von Neuman algebra generated by the regular ω-representation of G which is translation invariant in a certain sense. Analogues of the Fourier transformation, the Plancherel identity and the Fourier inversion formula are obtained in which this trace replaces the Haar measure on the dual group. 相似文献
11.
V. Manuilov 《Russian Journal of Mathematical Physics》2016,23(2):219-224
We consider pairs of mappings from a discrete group Γ to the unitary group. The deficiencies of these mappings from being homomorphisms may be great, but if they are close to each other, then we call such pairs balanced. We show that balanced pairs determine elements in the K 0 group of the classifying space of the group. We also show that a Fredholm representation of Γ determines balanced pairs. 相似文献
12.
Jacques Simon 《Letters in Mathematical Physics》1975,1(1):23-29
Given a Banach representation of a Hilbert Lie group, the Lie algebra \(\mathfrak{G}\) of which is the closure of the union of an increasing sequence of finite dimensional subalgebras, we construct a Gårding domain on which we differentiate the group representation to a representation of a dense subalgebra of \(\mathfrak{G}\) . 相似文献
13.
In the case of a finite-dimensional Hilbert space, it is shown that quantum mechanics can be embedded into discrete classical probability theory. In particular, states can be represented as stochastic vectors and observables as random variables such that all probabilities and expectation values are given in classical terms. 相似文献
14.
Let G be an exponential solvable Lie group and H an analytic subgroup of G. Let x be a unitary character of H and τ = Ind
H
G
χ. We provide a necessary and a sufficient condition for the representation τ to split finitely on its isotopic components
for adapted triplets. For the case in which H is maximal, we provide a concrete and smooth intertwining operator and its inverse for the disintegration of τ into irreducibles.
Research supported by the D.G.R.S.T., Unity 00/UR/15-01. 相似文献
15.
S. N. M. Ruijsenaars 《Communications in Mathematical Physics》1988,115(1):127-165
We construct an action-angle transformation for the Calogero-Moser systems with repulsive potentials, and for relativistic generalizations thereof. This map is shown to be closely related to the wave transformations for a large classl of Hamiltonians, and is shown to have remarkable duality properties. All dynamics inl lead to the same scattering transformation, which is obtained explicitly and exhibits a soliton structure. An auxiliary result concerns the spectral asymptotics of matrices of the formM exp(tD) ast→∞. It pertains to diagonal matricesD whose diagonal elements have pairwise different real parts and to matricesM for which certain principal minors are non-zero. 相似文献
16.
We discuss finite-dimensional representations of the homogeneous Galilei group which, when restricted to its subgroup SO(3), are decomposed to spin 0, 1/2 and 1 representations. In particular we explain how these representations were obtained in our paper (M. de Montigny et al.: J. Phys. A39 (2006) 9365) via reduction of the classification problem to a matrix one admitting exact solutions, and via contraction of the corresponding representations of the Lorentz group. Finally, for discussed representations we derive all functional invariants. 相似文献
17.
R. Hermann 《Communications in Mathematical Physics》1966,2(1):155-164
A method for constructing representations of non-compact semisimple groups from representations of semidirect product groups is presented. Necessary and sufficient algebraic conditions for the method to work are given, and these are applied to cases of possible interest for the classification of elementary particles.This work was supported by the Office of Naval Research, # NONR 3656 (09). 相似文献
18.
We classify the analytic actions, having a fixed point, of the classical inhomogeneous groups, such that the linear part of this action restricted to a Levi factor is the natural action defining this Levi factor as a classical simple group. 相似文献
19.
W. Siegel 《Physics letters. [Part B]》1984,134(5):318-320
By means of duality transformations we obtain representations of Yang-Mills groups which are neither tensors nor gauge fields, and fields which under general coordinate transformations are neither tensors nor tensor densities. 相似文献
20.
E. J. Woods 《Communications in Mathematical Physics》1970,17(1):1-20
We prove that a given representation of the canonical commutation relations can be extended uniquely by continuity to larger test function spaces which are maximal in the sense that no further extension is possible. For irreducible tensor product representations of the canonical commutation relations we give a necessary and a sufficient condition for the admissible test functions. We consider the problem of finding topologies on the test function spaces such that this extension can be obtained by a topological completion. Various examples are discussed.Supported in part by the National Research Council of Canada.An earlier version of the present work was distributed as a preprint entitled Topologies for Test Function Spaces for Representations of the Canonical Commutation Relations. 相似文献