×

zbMATH — the first resource for mathematics

Discrete series for semisimple Lie groups. II: Explicit determination of the characters. (English) Zbl 0199.20102

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Borel, A. &Harish-Chandra, Arithmetic subgroups of algebraic groups.Ann. of Math., 75 (1962), 485–535. · Zbl 0107.14804 · doi:10.2307/1970210
[2] Bruhat, F., Sur les représentations induites des groupes de Lie.Bull. Soc. Math. France, 84 (1956), 97–205. · Zbl 0074.10303
[3] Gindikin, S. G. &Karpelevič, F. I., Plancherel measure of Riemannian symmetric spaces of nonpositive curvature.Soviet Math., 3 (1962), 962–965. · Zbl 0156.03201
[4] Harish-Chandra, (a) Representations of a semisimple Lie group on a Banach space, I.Trans. Amer. Math. Soc., 75 (1953), 185–243. · Zbl 0051.34002 · doi:10.1090/S0002-9947-1953-0056610-2
[5] – (b) Representations of semisimple Lie groups, III.Trans. Amer. Math. Soc., 76 (1954), 234–253. · Zbl 0055.34002 · doi:10.1090/S0002-9947-1954-0062747-5
[6] – (c) Representations of semisimple Lie groups, V.Amer. J. Math., 78 (1956), 1–41. · Zbl 0070.11602 · doi:10.2307/2372481
[7] – (d) Representations of semisimple Lie groups, VI.Amer. J. Math., 78 (1956), 564–628. · Zbl 0072.01702 · doi:10.2307/2372674
[8] – (e) The characters of semisimple Lie groups.Trans. Amer. Math. Soc., 83 (1956), 98–163. · Zbl 0072.01801 · doi:10.1090/S0002-9947-1956-0080875-7
[9] – (f) Differential operators on a semisimple Lie algebra.Amer. J. Math., 79 (1957), 87–120. · Zbl 0072.01901 · doi:10.2307/2372387
[10] – (g) Fourier transforms on a semisimple Lie algebra, I.Amer. J. Math., 79 (1957), 193–257. · Zbl 0077.25205 · doi:10.2307/2372680
[11] – (h) Fourier transforms on a semisimple Lie algebra, II.Amer. J. Math., 79 (1957), 653–686. · Zbl 0079.32901 · doi:10.2307/2372569
[12] – (i) A formula for semisimple Lie groups.Amer. J. Math., 79 (1957), 733–760. · Zbl 0080.10201 · doi:10.2307/2372432
[13] – (j) Spherical functions on a semisimple Lie group, I.Amer. J. Math., 80 (1958), 241–310. · Zbl 0093.12801 · doi:10.2307/2372786
[14] – (k) Spherical functions on a semisimple Lie group, II.Amer. J. Math., 80 (1958), 553–613. · Zbl 0093.12801 · doi:10.2307/2372772
[15] – (l) Invariant eigendistributions on semisimple Lie groups.Bull. Amer. Math. Soc., 69 (1963), 117–123. · Zbl 0115.10801 · doi:10.1090/S0002-9904-1963-10889-7
[16] – (m) Invariant distributions on Lie algebras.Amer. J. Math., 86 (1964), 271–309. · Zbl 0131.33302 · doi:10.2307/2373165
[17] – (n) Some results on an invariant integral on a semisimple Lie algebra.Ann. of Math., 80 (1964), 551–593. · Zbl 0152.13401 · doi:10.2307/1970664
[18] – (o) Invariant eigendistributions on a semisimple Lie group.Trans. Amer. Math. Soc., 119 (1965), 457–508. · Zbl 0199.46402 · doi:10.1090/S0002-9947-1965-0180631-0
[19] – (p) Discrete series for semisimple Lie groups, I.Acta Math., 113 (1965), 241–318. · Zbl 0152.13402 · doi:10.1007/BF02391779
[20] – (q) Two theorems on semisimple Lie groups.Ann. of Math., 83 (1966), 74–128. · Zbl 0199.46403 · doi:10.2307/1970472
[21] Helgason, S., (a)Differential geometry and symmetric spaces. Academic Press, New York, 1962. · Zbl 0111.18101
[22] –, (b) Fundamental solutions of invariant differential operators on symmetric spaces.Amer. J. Math., 86 (1964), 565–601. · Zbl 0178.17001 · doi:10.2307/2373024
[23] Langlands, R. P., The dimension of spaces of automorphic forms.Amer. J. Math., 85 (1963), 99–125. · Zbl 0113.25802 · doi:10.2307/2373189
[24] Mackey, G. W., Infinite-dimensional group representations.Bull. Amer. Math. Soc., 69 (1963), 628–686. · Zbl 0136.11502 · doi:10.1090/S0002-9904-1963-10973-8
[25] Segal, I. E., Hypermaximality of certain operators on Lie groups.Proc. Amer. Math. Soc., 3 (1952), 13–15. · Zbl 0049.35704 · doi:10.1090/S0002-9939-1952-0051240-5
[26] Selberg, A., Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series.J. Indian Math. Soc., 20 (1956), 47–87. · Zbl 0072.08201
[27] Weyl, H., Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen, III.Math. Z., 24 (1926), 377–395. · JFM 52.0116.02 · doi:10.1007/BF01216789
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.