Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T08:18:04.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Irreducibility of some unitary representations of the poincaré group with respect to the Poincaré subsemigroup, II

Published online by Cambridge University Press:  22 January 2016

Hitoshi Kaneta
Hitoshi Kaneta*
Affiliation:
Department of Mathematics, Nagoya University
*
Department of Mathematics, Faculty of Education, Tokushima University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let P+(3) and P+(3) be the 3-dimensional space-time Poincaré group and the Poincaré subsemigroup, that is, P(3) = R3 × sSU(1, 1) and P+(3) = V+(3)=SSU(1, 1) where The multiplication is defined by the formula (x, g)(x′, g′) = (x + g*−1x′g−1, gg′) for x, x′ ∈ R3 and g, g′ ∈ SU(l, 1). Here x = (x0, x1, x2) is identified with the matrix

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 87 , November 1982 , pp. 147 - 174
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[1] Coddington, E. A. and Levinson, N., Theory of differential equations, McGraw-Hill, 1955.Google Scholar
[2] Diximier, J., C*-algebras (English translation), North-Holland, 1977.Google Scholar
[3] Gunning, R. C. and Rossi, H., Analytic functions of several complex variables, Prentice-Hall, 1965.Google Scholar
[4] Itatsu, S. and Kaneta, H., Spectral matrices for first and second order self-adjoint ordinary differential operators with long range potentials, Funkcialaj Ekvacioj, 24, no. 1 (1981), 23–45.Google Scholar
[5] Kaneta, H., Irreducibility of some unitary representations of the Poincaré group with respect to the Poincaré subsemigroup I, Nagoya Math. J., 78 (1980), 113–136.Google Scholar
[6] Kato, T., Perturbation theory for linear operators, Springer-Verlag, 1966.Google Scholar
[7] Mackey, G. W., Induced representations of locally compact groups I, Ann. of Math., 55 (1952), 101–139.Google Scholar
[8] Tatsuuma, N., Decomposition of representations of three-dimensional Lorentz group, Proc. Japan Acad., 36 (1962), 12–14.Google Scholar
[9] Titchmarsh, E. C., Introduction to the theory of Fourier integral, Oxford Univ. Press, 1937.Google Scholar
[10] Vilenkin, N., Special functions and the theory of group representation, AMS Translation Monograph 22, 1968.Google Scholar
[11] Yosida, K., Functional analysis, Springer-Verlag, 1965.Google Scholar