Infinitesimal isospectral deformations of the Grassmannian of 3-planes in 6  [ Déformations infinitésimales isospectrales de la grassmannienne des 3-plans dans 6  ] (2007)


Gasqui, Jacques; Goldschmidt, Hubert
Mémoires de la Société Mathématique de France, Tome 108 (2007) vi-92 p
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doi : 10.24033/msmf.420
URL stable : http://www.numdam.org/item?id=MSMF_2007_2_108__1_0

Bibliographie

[1] S. ArakiOn root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1964), p. 1–34. MR 153782

[2] N. BourbakiEléments de mathématique, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris, 1968. Zbl 0165.56403 | MR 132805

[3] W. Fulton & J. HarrisRepresentation theory: a first course, Graduate Texts in Math., vol. 129, Springer-Verlag, New York, Berlin, Heidelberg, 1991. Zbl 0744.22001 | MR 1153249

[4] J. Gasqui & H. GoldschmidtOn the geometry of the complex quadric, Hokkaido Math. J. 20 (1991), p. 279–312. Zbl 0764.53048 | MR 1114408

[5] —, Radon transforms and spectral rigidity on the complex quadrics and the real Grassmannians of rank two, J. Reine Angew. Math. 480 (1996), p. 1–69. Zbl 0861.53054 | | MR 1420557

[6] —, Radon transforms and the rigidity of the Grassmannians, Ann. of Math. Studies, no. 156, Princeton University Press, Princeton, NJ, Oxford, 2004. Zbl 1051.44003

[7] —, Infinitesimal isospectral deformations of the Lagrangian Grassmannians, Ann. Inst. Fourier (Grenoble) (to appear). Numdam | Zbl 1140.44001

[8] J. Gasqui, H. Goldschmidt & H. WilfSome summation identities and their computer proofs, 2004, Available online at http://www.cis.upenn.edu/wilf/GoldschmidtSummationQuestion.pdf.

[9] F. Gonzales & S. HelgasonInvariant differential operators on Grassmann manifolds, Adv. in Math. 60 (1986), p. 81–91. Zbl 0613.58038 | MR 839483

[10] R. Goodman & N. WallachRepresentations and invariants of the classical groups, Cambridge University Press, Cambridge, 1998. Zbl 0901.22001 | MR 1606831

[11] E. GrinbergOn images of Radon transforms, Duke. Math. J. 52 (1985), p. 939–972. Zbl 0623.44005 | MR 816395

[12] —, Aspects of flat Radon transforms, Contemp. Math. 140 (1992), p. 73–85. Zbl 0785.44002 | MR 1197589

[13] —, Flat Radon transforms on compact symmetric spaces with application to isospectral deformations, Preprint.

[14] V. GuilleminOn micro-local aspects of analysis on compact symmetric spaces, in Seminar on micro-local analysis, by V. Guillemin, M. Kashiwara and T. Kawai, Ann. of Math. Studies, no. 93, Princeton University Press, University of Tokyo Press, Princeton, NJ, 1979, p. 79–111. MR 560315

[15] S. HelgasonFundamental solutions of invariant differential operators on symmetric spaces, Amer. Math. J. 86 (1964), p. 565–601. Zbl 0178.17001 | MR 165032

[16] —, Differential geometry, Lie groups, and symmetric spaces, Academic Press, Orlando, FL, 1978.

[17] —, Some results on invariant differential operators on symmetric spaces, Amer. Math. J. 114 (1992), p. 769–811.

[18] —, Geometric analysis on symmetric spaces, Math. Surveys Monogr., vol. 39, American Mathematical Society, Providence, RI, 1994.

[19] R. MichelProblèmes d’analyse géométrique liés à la conjecture de Blaschke, Bull. Soc. Math. France 101 (1973), p. 17–69. Numdam | Zbl 0265.53041 | | MR 317231

[20] M. Petkovšek, H. Wilf & D. ZeilbergerA=B, A K Peters, Ltd., Wellesley, MA, 1996.

[21] R. StrichartzThe explicit Fourier decomposition of L 2 (SO(n)/SO(n-m)), Canad. J. Math. 27 (1975), p. 294–310. Zbl 0275.43009 | MR 380277

[22] C. TsukamotoInfinitesimal Blaschke conjectures on projective spaces, Ann. Sci. École Norm. Sup. (4) 14 (1981), p. 339–356. Numdam | Zbl 0481.53041 | | MR 644522

[23] T. VustOpération de groupes réductifs dans un type de cônes homogènes, Bull. Soc. Math. France 102 (1974), p. 317–333. Numdam | Zbl 0332.22018 | | MR 366941

[24] N. WallachReal reductive groups I, Academic Press, Boston, San Diego, 1988. Zbl 0666.22002 | MR 929683