Research
Research interests: Representation Theory of Reductive Groups and Hecke Algebras, Homological Algebra, Number Theory
Preprints:
(joint with D. Wong) On the Lefschetz principle for GL(n,C) and GL(n,Q_p), arXiv
Quotient branching law for p-adic (GL(n+1),GL(n)) I: generalized Gan-Gross-Prasad relevant pairs, 72 pages, arXiv Slides
On commutations of derivatives and integrals of $\square$-irreducible representations for p-adic GL, 29 pages, arXiv
On the product functor on inner forms of general linear group over a non-Archimedean field, 40 pages, arXiv
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):
Ext-multiplicity thoerem for standard representations of (GL(n+1), GL(n)),25 pages, arXiv Slides , Math. Z.
Restriction for general linear groups: the local non-tempered Gan-Gross-Prasad conjecture (non-Archimedean case), 42 pages, Crelles Journal, arXiv Slides Slides
Homological branching law for (GL(n+1,F),GL(n,F)): projectivity and indecomposability , Invent. Math. 225, pages 299–345 (2021), Slides , Slides
(with G. Savin) A vanishing Ext-branching theorem for (GL(n+1,F),GL(n,F)), arXiv, Duke Math. Journal, 170(10): 2237-2261
(with G. Savin) Iwahori components of Bessel model spaces, Proc. Amer. Math. Soc. 148 (2020), 1487-1497 , 10 pages, arXiv
(with G. Savin) Bernstein-Zelevinsky derivatives: a Hecke algebra approach , IMRN, , Volume 2019, Issue 3, February 2019, Pages 731–760, arXiv
(with G. Savin) Iwahori component of the Gelfand Graev representation, Math. Z. 288, 125–133 (2018).
A vanishing theorem for Dirac cohomology of standard modules , (2018), Adv. Math., 2018, 325, 274-311, arXiv
Some methods of computing first extensions between modules of graded Hecke algebras , Algebras and Representation Theory (2017), arXiv
Duality for Ext-groups and extensions of discrete series for graded Hecke algebras , Adv. Math., 2016, 294, 410-453, arXiv
Dirac cohomology for degenerate affine Hecke-Clifford algebras , Transformation Groups, 2017, 38 pages arXiv
Spin representations of real reflection groups of noncrystallographic root systems, J. Algebra , 2013, 379, 333-354. arXiv
(with H. F. Law, P. P. W. Wong) On polar ovals in abelian projective planes , Inov. Incidence Geom., 2011, 12, 35-48.
(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:
PhD thesis: Extensions of graded affine Hecke algebra modules
Others:
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"
(with G. Savin) Bernstein-Zelevinsky derivatives, branching rules and Hecke algebras, preprint (2016), arXiv, this preprint has been replaced by other work
(with L. Rider, P. Sobaje) Exotic t-structure for partial resolution of nilpotent cones, 18 pages, under revision arXiv