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A duality for symmetric spaces with applications to group representations.(English)Zbl 0209.25403


MSC:

53C35 Differential geometry of symmetric spaces
57T15 Homology and cohomology of homogeneous spaces of Lie groups
20C99 Representation theory of groups

Cite

References:

[1]Agmon, S., Lectures on Elliptic Boundary Value Problems (1965), Van Nostrand Co., Inc: Van Nostrand Co., Inc Princeton, N. J ·Zbl 0151.20203
[2]Araki, S., On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka Univ., 13, 1-34 (1962) ·Zbl 0123.03002
[3]Bhanu-Murthy, T. S., Plancherel’s measure for the factor space \(SL(n, R) SO(n, R)\), Dokl. Akad. Nauk. SSSR, 133, 503-506 (1960) ·Zbl 0097.10903
[4]Bhanu-Murthy, T. S., The asymptotic behaviour of zonal spherical functions on the Siegel upper half plane, Dokl. Akad. Nauk. SSSR, 135, 1027-1030 (1960)
[5]Blattner, R., On induced representations II: Infinitesimal induction, Amer. J. Math., 83, 499-512 (1961) ·Zbl 0139.07702
[6]Bourbaki, N., Éléments de Mathématique, Vol. VI, Intégration, (1952), Hermann: Hermann Paris, Chaps. I-V ·Zbl 0049.31703
[7]Bruhat, F., Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France, 84, 97-205 (1956) ·Zbl 0074.10303
[8]Bruhat, F., Sur les représentations des groupes \(p\)-adiques, Amer. J. Math., 83, 343-368 (1961) ·Zbl 0107.02504
[9]Cartan, H.; Serre, J.-P., Un théorème de finitude concernant les variétés analytiques compactes, C.R. Acad. Sci. Paris, 237, 128-130 (1953) ·Zbl 0050.17701
[10]Chern, S. S., On integral geometry in Klein spaces, Ann. Math., 43, 178-189 (1942) ·JFM 68.0462.02
[11]Ehrenpreis, L.; Mautner, F., Some properties of the Fourier transform on semisimple Lie groups, I, Ann. of Math., 61, 406-439 (1955) ·Zbl 0066.35701
[12]Erdélyi, A., Higher Transcendental Functions, (Bateman manuscript project, Vol. I (1953), McGraw-Hill Book Co: McGraw-Hill Book Co New York) ·Zbl 0143.29202
[13]Furstenberg, H., Translation-invariant cones of functions on semisimple Lie groups, Bull. Amer. Math. Soc., 71, 271-326 (1965) ·Zbl 0178.16901
[14]Gangolli, R., Isotropic infinitely divisible measures on symmetric spaces, Acta Math., 111, 213-246 (1964) ·Zbl 0154.43804
[15]R. Gangolli;R. Gangolli ·Zbl 0232.43007
[16]Gelfand, I. M., Integral geometry and its relation to group representations, Russian Math. Surveys, 143-151 (1960) ·Zbl 0119.17701
[17]Gelfand, I. M.; Graev, M. I., The geometry of homogeneous spaces, group representations in homogeneous spaces and questions in integral geometry related to them, Amer. Math. Soc. Transl., 37, 351-429 (1964) ·Zbl 0136.43404
[18]Gelfand, I. M.; Graev, M. I.; Pyatetskii-Shapiro, I. I., Representation Theory and Automorphic Functions (1969), W. B. Saunders Co: W. B. Saunders Co Philadelphia, Pa ·Zbl 0177.18003
[19]Gelfand, I. M.; Graev, M. I.; Shapiro, S. J., Differential forms and integral geometry, Functional Anal. Appl., 3, 24-40 (1969) ·Zbl 0191.52802
[20]Gelfand, I. M.; Graev, M. I.; Vilenkin, N., Integral Geometry and Representation Theory, (Generalized Functions, Vol. 5 (1966), Academic Press, Inc: Academic Press, Inc New York) ·Zbl 1339.01005
[21]Gelfand, I. M.; Naimark, M. A., Unitäre Darstellungen der klassischen Gruppen (1957), Akademie Verlag: Akademie Verlag Berlin, Germany ·Zbl 0077.03405
[22]Gindikin, S. G.; Karpelevič, F. I., Plancherel measure of Riemannian symmetric spaces of nonpositive curvature, Sov. Math., 3, 962-965 (1962) ·Zbl 0156.03201
[23]Gindikin, S. G.; Karpelevič, F. I., On a Problem in Integral Geometry (1964), Kazan University, Chebotarev Memorial Vol. ·Zbl 0505.53032
[24]Godement, R., A theory of spherical functions, Trans. Amer. Math. Soc., 73, 496-556 (1952) ·Zbl 0049.20103
[25]Godement, R., Introduction aux Travaux de Selberg, (Séminaire Bourbaki (1957)) ·Zbl 0202.40902
[26]Harish-Chandra, Representations of a semisimple Lie group on a Banach space I, Trans. Amer. Math. Soc., 75, 185-243 (1953) ·Zbl 0051.34002
[27]Harish-Chandra, On the Plancherel formula for the right-invariant functions on a semisimple Lie group, (Proc. Nat. Acad. Sci. USA, 40 (1954)), 200-204 ·Zbl 0055.10303
[28]Harish-Chandra, Representations of semisimple Lie groups III, Trans. Amer. Math. Soc., 76, 234-253 (1954) ·Zbl 0055.34002
[29]Harish-Chandra, The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc., 76, 485-528 (1954) ·Zbl 0055.34003
[30]Harish-Chandra, Representations of semisimple Lie groups IV, Amer. J. Math., 77, 743-777 (1955) ·Zbl 0066.35603
[31]Harish-Chandra, The characters of semisimple Lie groups, Trans. Amer. Math. Soc., 83, 98-163 (1956) ·Zbl 0072.01801
[32]Harish-Chandra, On a lemma of Bruhat, J. Math. Pures Appl., 35, 203-210 (1956) ·Zbl 0070.26004
[33]Harish-Chandra, Differential operators on a semisimple Lie algebra, Amer. J. Math., 79, 87-120 (1957) ·Zbl 0072.01901
[34]Harish-Chandra, Spherical functions on a semisimple Lie group I, Amer. J. Math., 80, 241-310 (1958) ·Zbl 0093.12801
[35]Harish-Chandra, Spherical functions on a semisimple Lie group II, Amer. J. Math., 80, 553-613 (1958) ·Zbl 0093.12801
[36]Harish-Chandra, Discrete series for semisimple Lie groups II, Acta Math., 116, 1-111 (1966) ·Zbl 0199.20102
[37]Harish-Chandra, Harmonic analysis on semisimple Lie groups, (Amer. Math. Soc. Colloquium Lectures (1969)) ·Zbl 0201.46002
[38]Helgason, S., Differential operators on homogeneous spaces, Acta Math., 102, 239-299 (1959) ·Zbl 0146.43601
[39]Helgason, S., Differential Geometry and Symmetric Spaces (1962), Academic Press, Inc: Academic Press, Inc New York ·Zbl 0122.39901
[40]Helgason, S., Duality and Radon transform for symmetric spaces, Amer. J. Math., 85, 667-692 (1963) ·Zbl 0124.05203
[41]Helgason, S., A duality in integral geometry; some generalizations of the Radon transform, Bull. Amer. Math. Soc., 70, 435-446 (1964) ·Zbl 0173.50502
[42]Helgason, S., Fundamental solutions of invariant differential operators on symmetric spaces, Amer. J. Math., 86, 565-601 (1964) ·Zbl 0178.17001
[43]Helgason, S., The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math., 113, 153-180 (1965) ·Zbl 0163.16602
[44]Helgason, S., Radon-Fourier transforms on symmetric spaces and related group representations, Bull. Amer. Math. Soc., 71, 757-763 (1965) ·Zbl 0163.37001
[45]Helgason, S., A Duality in Integral Geometry on Symmetric Spaces, (Proc. U.S.-Japan Seminar in Differential Geometry. Proc. U.S.-Japan Seminar in Differential Geometry, Kyoto, Japan (1965)), 37-56 ·Zbl 0141.39105
[46]Helgason, S., An analog of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces, Math. Ann., 165, 297-308 (1966) ·Zbl 0178.17101
[47]Helgason, S., Lie Groups and Symmetric Spaces, (Battelle Rencontres 1967 (1968), W. A. Benjamin, Inc: W. A. Benjamin, Inc New York), 1-71 ·Zbl 0209.25403
[48]Helgason, S., Applications of the Radon transform to representations of semisimple Lie groups, (Proc. Nat. Acad. Sci. USA, 63 (1969)), 643-647 ·Zbl 0188.45203
[49]Helgason, S.; Johnson, K., The bounded spherical functions on symmetric spaces, Advan. Math., 3, 586-593 (1969) ·Zbl 0188.45405
[50]Iwahori, N., On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo, 10, 215-236 (1964) ·Zbl 0135.07101
[51]Karpelevič, F. I., The geometry of geodesics and the eigenfunctions of the Beltrami-Laplace operator on symmetric spaces, Trans. Moscow Math. Soc., 14, 48-185 (1965) ·Zbl 0156.42002
[52]Knapp, A. W.; Stein, E. M., Singular integrals and the principal series, (Proc. Nat. Acad. Sci. USA, 63 (1969)), 281-284 ·Zbl 0181.12501
[53]A. W. Knapp and E. M. SteinProc. Nat. Acad. Sci.;A. W. Knapp and E. M. SteinProc. Nat. Acad. Sci. ·Zbl 0201.14702
[54]A. W. Knapp and E. M. Stein;A. W. Knapp and E. M. Stein ·Zbl 0208.38001
[55]Kodaira, K., On a differential-geometric method in the theory of analytic stacks, (Proc. Nat. Acad. Sci. USA, 39 (1953)), 865-868 ·Zbl 0051.14502
[56]Kostant, B., On the conjugacy of real Cartan subalgebras, (Proc. Nat. Acad. Sci. USA, 41 (1955)), 967-970 ·Zbl 0065.26901
[57]Kostant, B., On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc., 75, 627-642 (1969) ·Zbl 0229.22026
[58]Köthe, G., Die Randverteilungen analytischer Funktionen, Math. Z., 57, 13-33 (1952) ·Zbl 0047.35203
[59]Kunze, R. A.; Stein, E. M., Uniformly bounded representations III, Amer. J. Math., 89, 385-442 (1967) ·Zbl 0195.14202
[60]Lions, J. L.; Magenes, E., Problèmes aux limits non homogènes VII, Ann. Math. Pura Appl., 63, 4, 201-224 (1963) ·Zbl 0126.31103
[61]Loos, O., (Symmetric Spaces, Vol. II (1969), W. A. Benjamin, Inc: W. A. Benjamin, Inc New York) ·Zbl 0149.41004
[62]Mackey, G. W., Induced representations of locally compact groups I, Ann. Math., 55, 101-140 (1952) ·Zbl 0046.11601
[63]Matsumoto, H., Fonctions sphériques sur un groupe semisimple \(p\)-adique, C.R. Acad. Sci. Paris, 269, 829-832 (1969) ·Zbl 0189.44802
[64]Mautner, F. I., Fourier analysis and symmetric spaces, (Proc. Nat. Acad. Sci. USA, 37 (1951)), 529-533 ·Zbl 0043.26303
[65]Mautner, F. I., Spherical functions over \(p\)-adic fields I, Amer. J. Math., 80, 441-457 (1958) ·Zbl 0092.12501
[66]MacDonald, I., Spherical functions on a \(p\)-adic Chevalley group, Bull. Amer. Math. Soc., 74, 520-525 (1968) ·Zbl 0273.22012
[67]Mostow, G. D., Some new decomposition theorems for semisimple Lie groups, Mem. Amer. Math. Soc., 14, 31-54 (1955) ·Zbl 0064.25901
[68]Parthasarathy, K. R.; Ranga Rao, R.; Varadarajan, V. S., Representations of complex semisimple Lie groups and Lie algebras, Ann. Math., 85, 383-429 (1967) ·Zbl 0177.18004
[69]Satake, I., On representations and compactifications of symmetric Riemann spaces, Ann. Math., 71, 77-110 (1960) ·Zbl 0094.34603
[70]Schiffmann, G., Intégrales d’entrelacement, C.R. Acad. Sci. Paris, 266, 47-49 (1968) ·Zbl 0225.22024
[71]Schiffmann, G., Sur les Intégrales d’entrelacement de R. A. Kunze et E. M. Stein, (Thése (1969)), Paris
[72]Schwartz, L., Théorie des Distributions (1966), Hermann and Co: Hermann and Co Paris ·Zbl 0149.09501
[73]Semyanistyi, V. I., Homogeneous functions and some problems in integral geometry in spaces of constant curvature, Soviet Math., 2, 59-62 (1961) ·Zbl 0100.36602
[74]Serre, J.-P., Représentations Linéaires et Espaces Homogènes Kähleriens des Groupes de Lie Compacts, (Sém. Bourbaki (1954)) ·Zbl 0121.16203
[75](Séminaire Sophus Lie, Théorie des algèbres de Lie, Topologie des groupes de Lie. Séminaire Sophus Lie, Théorie des algèbres de Lie, Topologie des groupes de Lie, Paris (1955)) ·Zbl 0068.02102
[76]Steinberg, R., Differential equations invariant under finite reflection groups, Trans. Amer. Math. Soc., 112, 392-400 (1964) ·Zbl 0196.39202
[77]Stern, A. I., Completely irreducible class I representations of real semisimple Lie groups, Soviet Math., 20, 1254-1257 (1969) ·Zbl 0196.15402
[78]Tahahashi, R., Sur les représentations unitaires des groupes de Lorentz généralisées, Bull. Soc. Math. France, 91, 289-433 (1963) ·Zbl 0196.15501
[79]Wallach, N., Induced representations of Lie algebras and a theorem of Borel-Weil, Trans. Amer. Math. Soc., 136, 181-187 (1969) ·Zbl 0294.17005
[80]Zhelobenko, D. P., The theory of linear representations of complex and real Lie groups, Trans. Moscow Math. Soc., 12, 57-110 (1963) ·Zbl 0136.29802
[81]Zhelobenko, D. P., Symmetry in the class of elementary representations of a semisimple Lie group, Functional Anal. Appl., 1, 15-38 (1967) ·Zbl 0192.36003
[82]Zhelobenko, D. P., Analogue of the Cartan-Weyl theory for infinite-dimensional representations of semisimple complex Lie group, Soviet Math., 8, 798-801 (1967) ·Zbl 0188.20003
[83]Zhelobenko, D. P., The analysis of irreducibility in the class of elementary representations of a complex semisimple Lie group, Izv. Akad. Nauk SSSR, 32, 105-128 (1968) ·Zbl 0205.04404
[84]Zhelobenko, D. P.; Naimark, M. A., A characterization of completely irreducible representations of a semisimple complex Lie group, Soviet Math., 7, 1403-1406 (1966) ·Zbl 0315.22009
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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