Research

Upcoming event: HKU Number Theory Days 2024 with Frontiers of Mathematics Lecture

Research interests: Representation Theory of Reductive Groups and Hecke Algebras, Homological Algebra, Number Theory

Papers on arXiv  ORCID

Preprints:

1. Dual of the geometric lemma and the second adjointness for p-adic reductive groups, arXiv

2. (joint with D. Wong) On the Lefschetz principle for GL(n,C) and GL(n,Q_p), arXiv

3. Quotient branching law for p-adic (GL(n+1),GL(n)) I: generalized Gan-Gross-Prasad relevant pairs, 72 pages, arXiv Slides

4. Duality for generalized Gan-Gross-Prasad relevant pairs, 39 pages, arXiv 

5. On the product functor on inner forms of general linear group over a non-Archimedean field, 40 pages, arXiv

6. Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments, 90 pages, arXiv Slides latest versions: BZ1, BZ2,  BZ3, BZ4

Publications (including accepted papers):

1. Ext-multiplicity thoerem for standard representations of (GL(n+1), GL(n)),25 pages,   arXiv Slides , Math. Z.

2. Restriction for general linear groups: the local non-tempered Gan-Gross-Prasad conjecture (non-Archimedean case), 42 pages, Crelles Journal, arXiv Slides  Slides

3. Homological branching law for (GL(n+1,F),GL(n,F)): projectivity and indecomposability , Invent. Math.  225, pages 299–345 (2021),  Slides , Slides

4. (with G. Savin) A vanishing Ext-branching theorem for (GL(n+1,F),GL(n,F)), arXiv,  Duke Math. Journal, 170(10): 2237-2261 

5. (with G. Savin) Iwahori components of Bessel model spaces,  Proc. Amer. Math. Soc. 148 (2020), 1487-1497 , 10 pages, arXiv

6. (with G. Savin) Bernstein-Zelevinsky derivatives: a Hecke algebra approach ,  IMRN, , Volume 2019, Issue 3, February 2019, Pages 731–760, arXiv 

7. (with G. Savin) Iwahori component of the Gelfand Graev representation, Math. Z. 288, 125–133 (2018). 

8. A vanishing theorem for Dirac cohomology of standard modules , (2018), Adv. Math., 2018, 325, 274-311, arXiv

9. Some methods of computing first extensions between modules of graded Hecke algebras , Algebras and Representation Theory (2017),  arXiv

10. Duality for Ext-groups and extensions of discrete series for graded Hecke algebras ,  Adv. Math., 2016, 294, 410-453, arXiv

11. Dirac cohomology for degenerate affine Hecke-Clifford algebras , Transformation Groups, 2017, 38 pages arXiv

12. Spin representations of real reflection groups of noncrystallographic root systems, J. Algebra , 2013, 379, 333-354. arXiv

13. (with H. F. Law, P. P. W. Wong) On polar ovals in abelian projective planes , Inov. Incidence Geom., 2011, 12, 35-48.

14. (with J-H. Lu and S. K-M. To) On intersections of conjugacy classes and Bruhat cells , Trans. groups , 2010, 15 (2), 243-260. arXiv

PhD thesis:

1. PhD thesis: Extensions of graded affine Hecke algebra modules

Others:

1. On a twisted Euler-Poincare pairing for graded affine Hecke algebras, preprint  Part of this article was  incorporated to the article "Duality for Ext-groups and extensions of discrete series for graded Hecke algebras"

2. (with G. Savin) Bernstein-Zelevinsky derivatives, branching rules and Hecke algebras, preprint (2016), arXiv, this preprint has been replaced by other work

3. (with L. Rider, P. Sobaje) Exotic t-structure for partial resolution of nilpotent cones, 18 pages, under revision arXiv