Research interests

  • Representation theory of Lie groups and Lie algebras
    • Branching laws for unitary representations
    • Intertwining operators and multiplicities
    • Harmonic analysis on homogeneous spaces
  • Connections to
    • Number theory and Automorphic forms
    • Boundary value problems and Poisson transforms
    • Special functions and spectral decompositions

Preprints

  • An extension problem related to the fractional Branson-Gover operators (joint w/ B. Ørsted, G. Zhang)
    preprint (2019), available at arXiv:1904.03073.
  • Symmetry breaking operators for real reductive groups of rank one (joint w/ C. Weiske)
    preprint (2018), available at arXiv:1812.00697.
  • Appendix to Holomorphic torsion with coefficients and geometric zeta functions for certain Hermitian locally symmetric manifolds (by H. Moscovici and R. Stanton)
    preprint (2018), available at arXiv:1802.08886.
  • A minimal representation of the orthosymplectic Lie superalgebra (joint w/ S. Barbier)
    preprint (2017), available at arXiv:1710.07271.
  • Symmetry breaking operators for strongly spherical reductive pairs
    preprint (2017), available at arXiv:1705.06109.
  • Knapp-Stein type intertwining operators for symmetric pairs II. - The translation principle and intertwining operators for spinors (joint w/ B. Ørsted)
    preprint (2017), available at arXiv:1702.02326.

Publications

  1. The compact picture of symmetry breaking operators for rank one orthogonal and unitary groups (joint w/ B. Ørsted)
    to appear in Pacific J. Math., available at arXiv:1404.1171.
  2. Symmetry breaking operators for line bundles over real projective spaces (joint w/ C. Weiske)
    J. Lie Theory 29 (2019), no. 2, 511-558.
  3. A Godement-Jacquet type integral and the metaplectic Shalika model (joint w/ E. Kaplan)
    Amer. J. Math. 141 (2019), no. 1, 219-282.
  4. Upper bounds for geodesic periods over rank one locally symmetric spaces (joint w/ F. Su)
    Forum Math. 30 (2018), no. 5, 1065-1077.
  5. The Berezin form on symmetric R-spaces and reflection positivity (joint w/ G. Ólafsson and B. Ørsted)
    Banach Center Publications 113 (2017), 135-168.
  6. Estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles (joint w/ B. Ørsted)
    Int. Math. Res. Not. IMRN 2017 (2017), no. 11, 3209-3236.
  7. Bessel operators on Jordan pairs and small representations of semisimple Lie groups (joint w/ B. Schwarz)
    J. Funct. Anal. 272 (2017), no. 5, 1892-1955.
  8. On boundary value problems for some conformally invariant differential operators (joint w/ B. Ørsted and G. Zhang)
    Comm. Partial Differential Equations 41 (2016), no. 4, 609-643.
  9. Knapp-Stein type intertwining operators for symmetric pairs (joint w/ B. Ørsted and Y. Oshima)
    Adv. Math. 294 (2016), 256-306.
  10. Invariant differential operators on H-type groups and discrete components in restrictions of complementary series of rank one semisimple groups (joint w/ B. Ørsted and G. Zhang)
    J. Geom. Anal. 26 (2016), no. 1, 118-142.
  11. Restriction of most degenerate representations of O(1,N) with respect to symmetric pairs (joint w/ Y. Oshima)
    J. Math. Sci. Univ. Tokyo (Kodaira Centennial Issue) 22 (2015), no. 1, 279-338.
  12. Discrete branching laws for minimal holomorphic representations (joint w/ Y. Oshima)
    J. Lie Theory 25 (2015), no. 4, 949-983.
  13. Heat kernel analysis for Bessel operators on symmetric cones
    J. Lie Theory 24 (2014), no. 2, 373-396.
  14. Branching laws for small unitary representations of GL(n,C) (joint w/ B. Schwarz)
    Int. J. Math. 25 (2014), no. 6, 1450052.
  15. Minimal representations via Bessel operators (joint w/ J. Hilgert and T. Kobayashi)
    J. Math. Soc. Japan 66 (2014), no. 2, 349-414.
  16. Structure of the degenerate principal series on symmetric R-spaces and small representations (joint w/ B. Schwarz)
    J. Funct. Anal. 266 (2014), no. 6, 3508-3542.
  17. A geometric quantization of the Kostant-Sekiguchi correpondence for scalar type unitary highest weight representations
    Doc. Math. 18 (2013), 785-855.
  18. Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups (joint w/ J. Hilgert, T. Kobayashi and B. Ørsted)
    J. Funct. Anal. 263 (2012), no. 11, 3492-3563.
  19. Orthogonal polynomials associated to a certain fourth-order differential equation (joint w/ J. Hilgert, T. Kobayashi and G. Mano)
    Ramanujan J. 26 (2011), no. 3, 295-310.
  20. Special functions associated to a certain fourth-order differential equation (joint w/ J. Hilgert, T. Kobayashi and G. Mano)
    Ramanujan J. 26 (2011), no. 1, 1-34.
  21. An integral formula for L^2-eigenfunctions of a fourth-order Bessel-type differential operator (joint w/ T. Kobayashi)
    Integral Transforms Spec. Funct. 22 (2011), no. 7, 521-531.