My research in pictures

Research interests

  • Representations of real reductive groups

Research projects

  • Invariant distributions
  • Singular unitary representations
  • Degenerate principal series and local theta correspondence
  • Derived functor modules and transfer between real forms
  • Geometry of theta lifting
  • Local uniqueness of models
  • Local theta lifting of generalized Whittaker models
  • First occurrence and conservation relations
  • Special unipotent representations of real classical groups

Selected publications/preprints

  1. Invariant distributions of classical groups, Duke Math. Jour. 65 (1992), no. 1, 85-119.
  2. (with J.-S. Huang) On certain small representations of indefinite orthogonal groups, Representation Theory 1 (1997), 190-206.
  3. (with S. T. Lee) Degenerate principal series and local theta correspondence, Trans. Amer. Math. Soc. 350 (1998), no. 12, 5017-5046.
  4. (with N. Wallach) Transfer of unitary representations, Asian Jour. Math. 8 (2004), no. 4, 861-880 (special issue in memory of A. Borel).
  5. (with K. Nishiyama) Theta lifting of unitary lowest weight modules and their associated cycles, Duke Math. Jour. 125 (2004), no. 3, 415-465.
  6. (with D. Jiang and B. Sun) Uniqueness of Bessel models: the Archimedean case, Geom. Funct. Ana. 20 (2010), no. 3, 690-709.
  7. (with B. Sun) Multiplicity one theorems: the Archimedean case, Annals of Math. 175 (2012), no. 1, 23-44.
  8. (with R. Gomez) Local theta lifting of generalized Whittaker models associated to nilpotent orbits, Geom. Funct. Ana. 24 (2014), no. 3, 796-853.
  9. (with B. Sun) Conservation relations for local theta correspondence, J. Amer. Math. Soc. 28 (2015), no. 4, 939-983.
  10. (with J.-J. Ma and B. Sun) Unipotent representations of real classical groups, arXiv:1712.05552.

Books edited

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