On the Kronecker products of irreducible representations of the 2×2 real unimodular group. I

Pukánszky, Lajos

doi:10.1090/S0002-9947-1961-0172962-1

On the Kronecker products of irreducible representations of the $2\times 2$ real unimodular group. I

Author: Lajos Pukánszky
Journal: Trans. Amer. Math. Soc. 100 (1961), 116-152
MSC: Primary 22.57
DOI: https://doi.org/10.1090/S0002-9947-1961-0172962-1
MathSciNet review: 0172962
Full-text PDF Free Access

V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568–640. MR 21942, DOI https://doi.org/10.2307/1969129

E. T. Copson, An introduction to the theory of functions of a complex variable, Oxford, Clarendon Press, 1955.

I. M. Gel′fand and M. A. Naĭmark, Unitary representations of the Lorentz group, Izvestiya Akad. Nauk SSSR. Ser. Mat. 11 (1947), 411–504 (Russian). MR 0024440
George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI https://doi.org/10.2307/1969423

---, Induced representations of locally compact groups. II, Ann. of Math. vol. 58 (1953) pp. 193-220.

F. I. Mautner, Unitary representations of locally compact groups. II, Ann. of Math. (2) 52 (1950), 528–556. MR 36763, DOI https://doi.org/10.2307/1969431
F. I. Mautner, On the decomposition of unitary representations of Lie groups, Proc. Amer. Math. Soc. 2 (1951), 490–496. MR 41856, DOI https://doi.org/10.1090/S0002-9939-1951-0041856-3
F. J. Murray and J. Von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), no. 1, 116–229. MR 1503275, DOI https://doi.org/10.2307/1968693
John von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401–485. MR 29101, DOI https://doi.org/10.2307/1969463
M. A. Naĭmark, Decomposition of a tensor product of irreducible representations of the proper Lorentz group into irreducible representations. I. The case of a tensor product of representations of the fundamental series, Trudy Moskov. Mat. Obšč. 8 (1959), 121–153 (Russian). MR 0114139
I. E. Segal, A class of operator algebras which are determined by groups, Duke Math. J. 18 (1951), 221–265. MR 45133
I. E. Segal, Hypermaximality of certain operators on Lie groups, Proc. Amer. Math. Soc. 3 (1952), 13–15. MR 51240, DOI https://doi.org/10.1090/S0002-9939-1952-0051240-5
E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, at the Clarendon Press, 1946 (German). MR 0019765