Research

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

Papers on arXiv  ORCID

Preprints:

1. (with S. Huang) Discrete series for the graded Hecke algebra of type H4, 40pages, arXiv

2. (with B. Pattanayak) Algorithms for parabolic inductions and Jacquet moduels in GLn, 46 pages, arXiv

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

4. (joint with D. Wong) On the Lefschetz principle for GL(n,C) and GL(n,Q_p), arXiv, to appear in Israel Journal of Mathematics

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

6. Duality for generalized Gan-Gross-Prasad relevant pairs for p-adic GL, 39 pages, arXiv 

7. Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments I: Reduction to Combinatorics,  arXiv, to appear in Transactions of the AMS,  Slides  Sequels:, BZ2,  BZ3, BZ4

Publications (including accepted papers):

1. On the product functor on inner forms of general linear group over a non-Archimedean field, 40 pages, Transformation Groups (2024),  arXiv

2. Ext-multiplicity thoerem for standard representations of (GL(n+1), GL(n)),25 pages,   arXiv Slides , Math. Z. (2023)

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

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

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

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

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

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

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

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

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

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

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

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

15. (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