LieGA seminar

Co-organizer of Lie theory, geometry and analysis seminar

Research interests

Analysis and geometry on bounded symmetric domains, symmetric cones and causal symmetric spaces. Representation theory of semi-simple Lie groups. Jordan algebras and Jordan triple systems.

Publications

  • (with Abdelhamid Boussejra) Strichartz's conjecture for the Poisson transform and for generalized spectral projections on spinors. In preparation
  • (with Salem Ben Said and Jean-Louis Clerc) The source operators method : An overview. March 2023 (submitted) https://arxiv.org/abs/2307.12141
  • (with Salem Ben Said and Abdelhamid Boussejra) On Poisson transform for spinors. Tunisian J. Math. vol.5 (2023) no.4 pp. 771-792 https://doi.org/10.2140/tunis.2023.5.771 | https://arxiv.org/abs/2208.11763
  • (with Salem Ben Said and Abdelhamid Boussejra) On Poisson transforms for differential forms on real hyperbolic spaces. December 2021. https://arxiv.org/abs/2112.09994
  • (with Hideyuki Ishi) The semigroup associated to a certain non-symmetric homogeneous cone. Springer Proceedings in Mathematics & Statistics. Geometric and Harmonic Analysis on Homogeneous Spaces and Applications (2021) pp 123-136 https://doi.org/10.1007/978-3-030-78346-4_8 | pdf
  • (with Jean-Louis Clerc) Symmetry breaking differential operators for tensor products of spinorial representations. SIGMA 17 (2021), 049, 23 pages, https://doi.org/10.3842/SIGMA.2021.049 or https://arxiv.org/abs/2012.09625
  • (with Salem Ben Said and Jean-Louis Clerc) Conformally covariant bi-differential operators for differential forms. Communications in Mathematical Physics; (2020), https://doi.org/10.1007/s00220-019-03431-6 or arXiv:1809.06290
  • (with Salem Ben Said and Jean-Louis Clerc) Conformally covariant bi-differential operators on a simple real Jordan albebra. International Mathematics Research Notices; Published 8 May 2018, https://doi.org/10.1093/imrn/rny082 or arXiv:1704.01817
  • Editor of "Analysis, Geometry and Representations on Lie Groups and Homogeneous Spaces". Seminar On Math Sciences, N.39, Keio Univ. (2016), (122 pp). MR3470116
  • (with Salem Ben Said and Genkai Zhang) Invariant trilinear forms on spherical principal series of real rank one semiseimple Lie groups. Internat. J. Math. 25 (2014), no. 3, 1450017, 35 pp.
  • (with Genkai Zhang) Hua operators and relative discrete series on line bundle over bounded symmetric domains. J. Funct. Anal. 262 (2012), 4140--4159.
  • The Schwarzian derivative on symmetric spaces of Cayley type. RIMS Kôkyûroku Bessatsu B36 (2012), 75-82.
  • Hua operators for bounded symmetric domains and their eigenspaces. Inst. Élie Cartan, 19 Université de Nancy, Institut Élie Cartan, Nancy, 2009, 141–149. ISBN: 978-2-903594-20-6
  • (with A. Boussejra) Characterization of Poisson integrals for non-tube bounded symmetric domains. Math. Pures Appl. 87 (2007) 438--451.
  • (with Jean-Louis Clerc) Primitive du cocycle de Maslov généralisé. in Math. Ann. 337 (2007) 91--138.
  • (with Gankai Zhang) Hua operators and Poisson transforms for bounded symmetric domains. J. Funct. Anal. 236 (2006), 546--580.
  • Analyse et géométrie des domaines bornés symétriques. Habilitation, November 2006.
  • Application of Hilbert's projective metric on symmetric cones. Acta Math Sinica. 12 (2006), 1467--1472.
  • Jordan algebras, geometry of Hermitian symmetric spaces and non-commutative Hardy spaces. Seminar on Mathematical Sciences, 33. Keio University, Department of Mathematics, Yokohama, 2005. 70 pp.
  • Contractions of angles in symmetric cones. Publ. RIMS, Kyoto Univ. 38 (2002), 227--243.
  • (with Bent Orsted) Hardy spaces on two-sheeted covering semigroups. J. of Lie Theory, 7 (1997), 245--267.
  • (with Bent Orsted) Espace de Hardy sur le semi-groupe métaplectique. C.R. Acad. Sci. Paris, 322 (1996), 113--116.
  • (with Bent Orsted) Function spaces on the Ol'shanskii semigroup and the Gelfand and Gindikin program. Ann. Ins. Fourier. 46 (1996), 1-34.
  • Semi-groupe de Lie associé à un cône symétrique, Ann. Inst. Fourier. 45 (1995), 1--29.
  • Réalisation des espaces symétriques de type Cayley. C. R. Acad. Sci. Paris. 318 (1994), 425--428.
* Some items can be sent on request.

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