The Plancherel formula for SU(p, q)

Takeshi HIRAI

doi:10.2969/jmsj/02220134

Takeshi HIRAI

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JOURNAL FREE ACCESS

1970 Volume 22 Issue 2 Pages 134-179

DOI https://doi.org/10.2969/jmsj/02220134

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Published: 1970 Received: April 01, 1969 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: TITLE Details: Wrong : The Plancherel formula for SU(p, q)
Right : The Plancherel formula for SU(p, q)

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France, 84 (1956), 97-205.
2) M. I. Graev, Unitary representations of real simple Lie groups (in Russian), Trudy Moskov. Mat. Obšc., 7 (1958), 335-389.
3) Harish-Chandra, (a) Representations of semisimple Lie groups. III, Trans. Amer. Math. Soc., 76 (1954), 234-253.
(b) Representations of semisimple Lie groups. VI, Amer. J. Math., 78 (1956), 564-628.
(c) A formula for semisimple Lie groups, Amer. J. Math., 79 (1957), 733-760.
(d) Some results on an invariant integral on a semi-simple Lie algebra, Ann. of Math., 80 (1964), 551-593.
(e) Invariant eigendistributions on a semisimple Lie group, Trans. Amer. Math. Soc., 119 (1965), 457-508.
(f) Discrete series for semisimple Lie groups. II, Acta Math., 116 (1966), 1-111.
(g) The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc., 76 (1954), 485-528.
4) T. Hirai, (a) The characters of irreducible representations of the Lorentz group of n-th order, Proc. Japan Acad., 41 (1965), 526-531.
(b) The Plancherel formula for the Lorentz group of n-th order, Proc. Japan Acad., 42 (1966), 323-326.
(c) Classification and the characters of irreducible representations of SU(p, 1), Proc. Japan Acad., 42 (1966), 907-912.
(d) Invariant eigendistributions on real simple Lie groups. I, (to appear in Japan. J. Math.).
(e) The characters of some induced representations of semisimple Lie groups, J. Math. Kyoto Univ., 8 (1968), 313-363.
5) K. Okamoto, On the Plancherel formula for some types of simple Lie groups, Osaka J. Math., 2 (1965), 247-282.
6) B. D. Romm, Analogy of the Plancherel formula for real unimodular group of n-th order (in Russian), Izv. Akad. Nauk SSSR, 29 (1965), 1147-1202.
7) M. Sugiura, Conjugate classes of Cartan subalgebras in real semisimple Lie algebras, J. Math. Soc. Japan, 11 (1959), 374-434.
8) R. Takahashi, Sur les fonctions sphériques et la formule de Plancherel dans le groupe hyperbolique, Japan. J. Math., 31 (1961), 55-90.
9) L. Pukanszky, (a) The Plancherel theorem of the 2×2 real unimodular group, Bull. Amer. Math. Soc., 69 (1963), 504-512. (b) The Plancherel formula for the universal covering group of SL(R, 2), Math. Ann., 156 (1964), 96-143.

Right : 1) F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France, 84 (1956), 97-205.
2) M. I. Graev, Unitary representations of real simple Lie groups (in Russian), Trudy Moskov. Mat. Obšc., 7 (1958), 335-389.
3) Harish-Chandra, (a) Representations of semisimple Lie groups. III, Trans. Amer. Math. Soc., 76 (1954), 234-253.
(b) Representations of semisimple Lie groups. VI, Amer. J. Math., 78 (1956), 564-628.
(c) A formula for semisimple Lie groups, Amer. J. Math., 79 (1957), 733-760.
(d) Some results on an invariant integral on a semi-simple Lie algebra, Ann. of Math., 80 (1964), 551-593.
(e) Invariant eigendistributions on a semisimple Lie group, Trans. Amer. Math. Soc., 119 (1965), 457-508.
(f) Discrete series for semisimple Lie groups. II, Acta Math., 116 (1966), 1-111.
(g) The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc., 76 (1954), 485-528.
4) T. Hirai, (a) The characters of irreducible representations of the Lorentz group of n-th order, Proc. Japan Acad., 41 (1965), 526-531.
(b) The Plancherel formula for the Lorentz group of n-th order, Proc. Japan Acad., 42 (1966), 323-326.
(c) Classification and the characters of irreducible representations of SU(p,1), Proc. Japan Acad., 42 (1966), 907-912.
(d) Invariant eigendistributions on real simple Lie groups. I, (to appear in Japan. J. Math.).
(e) The characters of some induced representations of semisimple Lie groups, J. Math. Kyoto Univ., 8 (1968), 313-363.
5) K. Okamoto, On the Plancherel formula for some types of simple Lie groups, Osaka J. Math., 2 (1965), 247-282.
6) B. D. Romm, Analogy of the Plancherel formula for real unimodular group of n-th order (in Russian), Izv. Akad. Nauk SSSR, 29 (1965), 1147-1202.
7) M. Sugiura, Conjugate classes of Cartan subalgebras in real semisimple Lie algebras, J. Math. Soc. Japan, 11 (1959), 374-434.
8) R. Takahashi, Sur les fonctions sphériques et la formule de Plancherel dans le groupe hyperbolique, Japan. J. Math., 31 (1961), 55-90.
9) L. Pukanszky, (a) The Plancherel theorem of the 2×2 real unimodular group, Bull. Amer. Math. Soc., 69 (1963), 504-512. (b) The Plancherel formula for the universal covering group of SL(R,2), Math. Ann., 156 (1964), 96-143.

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