# Research

**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**

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

**Books edited**

**Representations of Real and P-adic Groups**, Vol 2, Lecture Notes Series, Institute for Mathematical Sciences, NUS, edited by Eng-Chye Tan and Chen-Bo Zhu, World Scientific Publishing, 2004.**Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory**: In Honor of Roger E. Howe, Vol 12, Lecture Notes Series, Institute for Mathematical Sciences, NUS, edited by Jian-Shu Li, Eng-Chye Tan, Nolan Wallach and Chen-Bo Zhu, World Scientific Publishing, 2007.**Representation Theory, Number Theory, and Invariant Theory**, In Honor of Roger Howe on the Occasion of His 70th Birthday, Progress in Mathematics, Vol. 323, Jim Cogdell, Ju-Lee Kim and Chen-Bo Zhu (Eds.), BirkhĂ¤user Basel, 2017.

**YouTube videos**

- Unipotent representations of real classical groups (Conference on Representation Theory and Algebraic Geometry, In honor of Joseph Bernstein, 2017)