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Wallach, Nolan R.

The analytic continuation of the discrete series. II. (English) Zbl 0419.22018

Trans. Am. Math. Soc. 251, 19-37 (1979).
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Cited in 4 Reviews
Cited in 46 Documents

MSC:

22E46 Semisimple Lie groups and their representations
22E60 Lie algebras of Lie groups
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras

Keywords:

representation; semisimple Lie algebra; semisimple Lie group; irreducibility; unitarizability; holomorphic discrete series; highest weight
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\textit{N. R. Wallach}, Trans. Am. Math. Soc. 251, 19--37 (1979; Zbl 0419.22018)
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References:

[1] Harish-Chandra, Representations of semisimple Lie groups. IV, Amer. J. Math. 77 (1955), 743 – 777. · Zbl 0066.35603
[2] Harish-Chandra, Representations of semisimple Lie groups. VI. Integrable and square-integrable representations, Amer. J. Math. 78 (1956), 564 – 628. · Zbl 0072.01702
[3] SigurÄ’ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.
[4] R. Hotta and N. R. Wallach, On Matsushima’s formula for the Betti numbers of a locally symmetric space (to appear). · Zbl 0327.53032
[5] Calvin C. Moore, Compactifications of symmetric spaces. II. The Cartan domains, Amer. J. Math. 86 (1964), 358 – 378. · Zbl 0156.03202
[6] H. Rossi and M. Vergue, Analytic continuation of the holomorphic discrete series of a semi-simple Lie group (to appear). · Zbl 0356.32020
[7] Wilfried Schmid, Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen, Invent. Math. 9 (1969/1970), 61 – 80 (German). · Zbl 0219.32013
[8] N. R. Wallach, The analytic continuation of the discrete series. I, Trans. Amer. Math. Soc. · Zbl 0419.22017
[9] Nolan R. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, No. 19. · Zbl 0265.22022
[10] Nolan R. Wallach, Induced representations of Lie algebras. II, Proc. Amer. Math. Soc. 21 (1969), 161 – 166. · Zbl 0294.17006
[11] Nolan R. Wallach, On maximal subsystems of root systems, Canad. J. Math. 20 (1968), 555 – 574. · Zbl 0235.17007
[12] Norbert Wiener, The Fourier integral and certain of its applications, dover Publications, Inc., New York, 1959. · Zbl 0081.32102
[13] H. Weyl, The classical groups, Princeton Univ. Press, Princeton, N. J., 1946. (1939 ed., MR 1, 42.) · JFM 65.0058.02
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.