Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 3166045
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: D. A. Timashev
Title: Homogeneous spaces and equivariant embeddings
Additional book information: Encyclopaedia of Mathematical Sciences, Vol. 138, Invariant Theory and Transformation Groups, 8, Springer, Heidelberg, 2011, xxii+253 pp., ISBN 978-3-642-18398-0

References [Enhancements On Off] (What's this?)

  • Marcel Berger, Les espaces symétriques noncompacts, Ann. Sci. École Norm. Sup. (3) 74 (1957), 85–177 (French). MR 0104763
  • William Barker and Roger Howe, Continuous symmetry, American Mathematical Society, Providence, RI, 2007. From Euclid to Klein. MR 2362745, DOI 10.1090/mbk/047
  • Armand Borel, Les espaces hermitiens symétriques (French). Séminaire Bourbaki 1951/52.
  • Armand Borel, Groupes linéaires algébriques, Ann. of Math. (2) 64 (1956), 20–82 (French). MR 93006, DOI 10.2307/1969949
  • Armand Borel, Semisimple groups and Riemannian symmetric spaces, Texts and Readings in Mathematics, vol. 16, Hindustan Book Agency, New Delhi, 1998. MR 1661166
  • Armand Borel, Essays in the history of Lie groups and algebraic groups, History of Mathematics, vol. 21, American Mathematical Society, Providence, RI; London Mathematical Society, Cambridge, 2001. MR 1847105
  • Armand Borel and Lizhen Ji, Compactifications of symmetric and locally symmetric spaces, Mathematics: Theory & Applications, Birkhäuser Boston, Inc., Boston, MA, 2006. MR 2189882
  • Armand Borel and André Lichnerowicz, Espaces riemanniens et hermitiens symétriques, C. R. Acad. Sci. Paris 234 (1952), 2332–2334 (French). MR 48134
  • E. Cartan, Les groupes projectifs qui ne laissent invariante aucune multiplicité plane, Bull. Soc. Math. France 41 (1913), 53–96 (French). MR 1504700
  • Élie Cartan , Sur un théorème fundamental de M. H. Weyl. J. Math. Pures Appl. (9) 2 (1923), 167–192.
  • E. Cartan, Sur une classe remarquable d’espaces de Riemann, Bull. Soc. Math. France 54 (1926), 214–264 (French). MR 1504900
  • E. Cartan, Sur une classe remarquable d’espaces de Riemann. II, Bull. Soc. Math. France 55 (1927), 114–134 (French). MR 1504909
  • Elie Cartan, Sur certaines formes Riemanniennes remarquables des géométries à groupe fondamental simple, Ann. Sci. École Norm. Sup. (3) 44 (1927), 345–467 (French). MR 1509283
  • Élie Cartan, Sur la détermination d’un système orthogonal complet dans un espace de Riemann symétrique clos. Rend. Circ. Mat. Palermo 53 (1929), 217–252.
  • Élie Cartan, La théorie finis et continus et l’Analysis Situs. Mém. Sci. Math. XLII, Gauthier-Villars, Paris, 1930.
  • Élie Cartan, Les espaces riemanniens symétriques. Verh. Internat. Congr. Math. (1932), 152–161.
  • Élie Cartan, Sur les domaines bornés homogeènes de l’espace de $n$ variables complexes. Abb. Math. Sem. Univ. Hamburg 11 (1935), 116–162.
  • S. S. Chern and C. Chevalley, Élie Cartan and his mathematical work, Bull. Amer. Math. Soc. 58 (1852), 217–250.
  • Claude Chevalley, Algebraic Lie algebras, Ann. of Math. (2) 48 (1947), 91–100. MR 19603, DOI 10.2307/1969217
  • Claude Chevalley and Hsio-Fu Tuan, On algebraic Lie algebras, Proc. Nat. Acad. Sci. U.S.A. 31 (1945), 195–196. MR 12279, DOI 10.1073/pnas.31.7.195
  • S. Evens and B. F. Jones, On the wonderful compactification. Lecture note, arXiv:0801.0456v1.
  • Harish-Chandra, Representations of semisimple Lie groups. IV, Amer. J. Math. 77 (1955), 743–777. MR 72427, DOI 10.2307/2372596
  • Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
  • Joachim Hilgert and Gestur Ólafsson, Causal symmetric spaces, Perspectives in Mathematics, vol. 18, Academic Press, Inc., San Diego, CA, 1997. Geometry and harmonic analysis. MR 1407033
  • A. Hurwitz, Über die Erzeugung der Invarianten durch Integration. Nachr. Kgl. Gew. Wiss. Göttingen, Math.-Phys. Klasse 1897, 71–90.
  • Soji Kaneyuki, On classification of para-Hermitian symmetric spaces, Tokyo J. Math. 8 (1985), no. 2, 473–482. MR 827002, DOI 10.3836/tjm/1270151228
  • Soji Kaneyuki, Compactification of parahermitian symmetric spaces and its applications. II. Stratifications and automorphism groups, J. Lie Theory 13 (2003), no. 2, 535–563. MR 2003159
  • M. Kashiwara, A. Kowata, K. Minemura, K. Okamoto, T. Ōshima, and M. Tanaka, Eigenfunctions of invariant differential operators on a symmetric space, Ann. of Math. (2) 107 (1978), no. 1, 1–39. MR 485861, DOI 10.2307/1971253
  • Friedrich Knop, Weylgruppe und Momentabbildung, Invent. Math. 99 (1990), 1–23.
  • Friedrich Knop, The Luna-Vust theory of spherical embeddings, Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989) Manoj Prakashan, Madras, 1991, pp. 225–249. MR 1131314
  • Adam Korányi and Joseph A. Wolf, Realization of hermitian symmetric spaces as generalized half-planes, Ann. of Math. (2) 81 (1965), 265–288. MR 174787, DOI 10.2307/1970616
  • Joseph A. Wolf and Adam Korányi, Generalized Cayley transformations of bounded symmetric domains, Amer. J. Math. 87 (1965), 899–939. MR 192002, DOI 10.2307/2373253
  • Shoshichi Kobayashi and Tadashi Nagano, On filtered Lie algebras and geometric structures. I, J. Math. Mech. 13 (1964), 875–907. MR 0168704
  • H. Levy, Forma canonica dei $ds^2$ per i quali si annullano i simboli di Riemann a cinque indici. Rend. Acc. Lincei 3 (1926), 65–69.
  • S. Lie, Theorie der Transformation Gruppen I, II, III. Unter mitwirkung von F. Engels, Leipzig 1888, 1890, 1893.
  • Ottmar Loos, Symmetric spaces. I: General theory, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0239005
  • D. Luna and Th. Vust, Plongements d’espaces homogènes, Comment. Math. Helv. 58 (1983), no. 2, 186–245 (French). MR 705534, DOI 10.1007/BF02564633
  • George W. Mackey, The scope and history of commutative and noncommutative harmonic analysis, History of Mathematics, vol. 5, American Mathematical Society, Providence, RI; London Mathematical Society, London, 1992. MR 1171011, DOI 10.1090/mawrld/002
  • Hans Maass, Siegel’s modular forms and Dirichlet series, Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin-New York, 1971. Dedicated to the last great representative of a passing epoch. Carl Ludwig Siegel on the occasion of his seventy-fifth birthday. MR 0344198
  • Hiêú Nguyêñ, Weakly symmetric spaces and bounded symmetric domains, Transform. Groups 2 (1997), no. 4, 351–374. MR 1486036, DOI 10.1007/BF01234540
  • G. Ólafsson, Symmetric spaces of Hermitian type, Differential Geom. Appl. 1 (1991), no. 3, 195–233. MR 1244444, DOI 10.1016/0926-2245(91)90001-P
  • Gestur Ólafsson, Analytic continuation in representation theory and harmonic analysis, Global analysis and harmonic analysis (Marseille-Luminy, 1999) Sémin. Congr., vol. 4, Soc. Math. France, Paris, 2000, pp. 201–233 (English, with English and French summaries). MR 1822362
  • G. Ólafsson and A. Pasquale, Ramanujan’s Master theorem for the hypergeometric Fourier transform on root systems. Preprint, arXiv:1211.0024.
  • Toshio Ōshima, A realization of Riemannian symmetric spaces, J. Math. Soc. Japan 30 (1978), no. 1, 117–132. MR 477175, DOI 10.2969/jmsj/03010117
  • Toshio Ōshima, A definition of boundary values of solutions of partial differential equations with regular singularities, Publ. Res. Inst. Math. Sci. 19 (1983), no. 3, 1203–1230. MR 723467, DOI 10.2977/prims/1195182027
  • Toshio Ōshima and Jir\B{o} Sekiguchi, Eigenspaces of invariant differential operators on an affine symmetric space, Invent. Math. 57 (1980), no. 1, 1–81. MR 564184, DOI 10.1007/BF01389818
  • D. I. Panyushev, Complexity and rank of actions in invariant theory, J. Math. Sci. 95 (1999), 1925–1985.
  • F. Peter and H. Weyl, Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Math. Ann. 97 (1927), no. 1, 737–755 (German). MR 1512386, DOI 10.1007/BF01447892
  • Ichirô Satake, On representations and compactifications of symmetric Riemannian spaces, Ann. of Math. (2) 71 (1960), 77–110. MR 118775, DOI 10.2307/1969880
  • Ichirô Satake, Algebraic structures of symmetric domains, Kanô Memorial Lectures, vol. 4, Iwanami Shoten, Tokyo; Princeton University Press, Princeton, N.J., 1980. MR 591460
  • Henrik Schlichtkrull, Hyperfunctions and harmonic analysis on symmetric spaces, Progress in Mathematics, vol. 49, Birkhäuser Boston, Inc., Boston, MA, 1984. MR 757178, DOI 10.1007/978-1-4612-5298-6
  • I. Schur, Neue Anwendungen der Integralrechnung auf Probleme der Invariantentheorie. I, II. Sitzungsber. Preuss. Akad. Wiss. Berlin 1924, 189–208, 297–321.
  • A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 88511
  • D. A. Timashëv, Classification of $G$-manifolds of complexity $1$, Izv. Ross. Akad. Nauk Ser. Mat. 61 (1997), no. 2, 127–162 (Russian, with Russian summary); English transl., Izv. Math. 61 (1997), no. 2, 363–397. MR 1470147, DOI 10.1070/im1997v061n02ABEH000119
  • Dmitry A. Timashev, Homogeneous spaces and equivariant embeddings, Encyclopaedia of Mathematical Sciences, vol. 138, Springer, Heidelberg, 2011. Invariant Theory and Algebraic Transformation Groups, 8. MR 2797018, DOI 10.1007/978-3-642-18399-7
  • André Weil, On algebraic groups of transformations, Amer. J. Math. 77 (1955), 355–391. MR 74083, DOI 10.2307/2372535
  • André Weil, On algebraic groups and homogeneous spaces, Amer. J. Math. 77 (1955), 493–512. MR 74084, DOI 10.2307/2372637
  • H. Weyl, Zur Theorie der Darstellung der einfachen kontinuierlichen Gruppen, Sitzungsber. Preuss. Akad. Wiss. Berline, 1924, 338–345.
  • H. Weyl, Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen. I, II, II und Nachtrag, Math. Zeitschr. 23 (1925), 271–309, 24 (1926), 328–376, 377–395. 789–791.
  • H. Weyl, Zur Darstellungstheorie und Invariantenabzählung der Projektiven, der Komplex- und der Drehungsgruppe, Acta Math. 48 (1926), no. 3-4, 255–278 (German). MR 1555225, DOI 10.1007/BF02565334
  • Joseph A. Wolf, The action of a real semisimple group on a complex flag manifold. I. Orbit structure and holomorphic arc components, Bull. Amer. Math. Soc. 75 (1969), 1121–1237. MR 251246, DOI 10.1090/S0002-9904-1969-12359-1
  • Joseph A. Wolf, Fine structure of Hermitian symmetric spaces, Symmetric spaces (Short Courses, Washington Univ., St. Louis, Mo., 1969–1970), Pure and App. Math., Vol. 8, Dekker, New York, 1972, pp. 271–357. MR 0404716
  • Joseph A. Wolf, Spaces of constant curvature, 6th ed., AMS Chelsea Publishing, Providence, RI, 2011. MR 2742530, DOI 10.1090/chel/372
  • Joseph A. Wolf, Harmonic analysis on commutative spaces, Mathematical Surveys and Monographs, vol. 142, American Mathematical Society, Providence, RI, 2007. MR 2328043, DOI 10.1090/surv/142
  • O. S. Yakimova, Weakly symmetric spaces of semisimple Lie groups, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2 (2002), 57–60, 72 (Russian, with Russian summary); English transl., Moscow Univ. Math. Bull. 57 (2002), no. 2, 37–40. MR 1934062
  • Oksana Yakimova, Gelfand pairs, Bonner Mathematische Schriften [Bonn Mathematical Publications], vol. 374, Universität Bonn, Mathematisches Institut, Bonn, 2005. Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, 2004. MR 2206354
    •
    Review Information:

    Reviewer: Gestur Ólafsson
    Affiliation: Department of Mathematics, Louisiana State University
    Email: olafsson@math.lsu.edu
    Journal: Bull. Amer. Math. Soc. 51 (2014), 349-359
    DOI: https://doi.org/10.1090/S0273-0979-2013-01430-7
    Published electronically: September 18, 2013
    Additional Notes: The author acknowledges the support of NSF Grant DMS-1101337 during the preparation of this article.
    Review copyright: © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.