Research

Research interests

  • Representations of real reductive groups

My research in pictures

Theta correspondence and the orbit method (Sun and Zhu, for ICM2022)

Research projects

  • Invariant distributions
  • Singular unitary representations
  • Degenerate principal series and local theta correspondence
  • Explicit duality 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 J.-S. Li, A. Paul, E.-C. Tan) The explicit duality correspondence of (Sp(p,q),O ∗ (2n)), J. Funct. Anal. 200 (2003), no. 1, 71-100.
  5. (with N. Wallach) Transfer of unitary representations, Asian Jour. Math. 8 (2004), no. 4, 861-880 (special issue in memory of A. Borel).
  6. (with K. Nishiyama) Theta lifting of unitary lowest weight modules and their associated cycles, Duke Math. Jour. 125 (2004), no. 3, 415-465.
  7. (with D. Jiang and B. Sun) Uniqueness of Bessel models: the Archimedean case, Geom. Funct. Ana. 20 (2010), no. 3, 690-709.
  8. (with B. Sun) Multiplicity one theorems: the Archimedean case, Annals of Math. 175 (2012), no. 1, 23-44.
  9. (with R. Gomez) Local theta lifting of generalized Whittaker models associated to nilpotent orbits, Geom. Funct. Ana. 24 (2014), no. 3, 796-853.
  10. (with B. Sun) Conservation relations for local theta correspondence, J. Amer. Math. Soc. 28 (2015), no. 4, 939-983.
  11. (with D. M. Barbasch, J.-J. Ma and B. Sun) Special unipotent representations of real classical groups: counting and reduction to good parity, arXiv:2205.05266.
  12. (with D. M. Barbasch, J.-J. Ma and B. Sun) Special unipotent representations of real classical groups: construction and unitarity, arXiv:1712.05552.

Books edited

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