Genkai Zhang

Professor at Chalmers, Mathematical Sciences, Analysis and Probability Theory

Genkai Zhang is working on representation theory of Lie groups and analysis on locally symmetric spaces. Much of the fundamental symmetries in mathematics and physics can be described in terms of Lie groups of transformations on geometric objects and their manifestations are studied using representations of Lie groups as matrices. Locally symmetric spaces are manifolds with large numbers of local symmetries. This research is mainly to understand the geometric and analytic properties of the spaces such as variations of their shapes, their resonance frequencies and quantum states, to discover and eventually classify unitary representations. Recently Genkai Zhang has been working on branching rules in representation theory, which is also called symmetry breaking in physics. Genkai Zhang has collabrations with colleagues inEurope, China, Japan, South Korea and USA.

Source: chalmers.se

Projects

2010–2012

Radon transform. Harmonic and Complex Analysis on symmetric spaces. Representations of Lie groups.

Genkai Zhang Analysis and Probability Theory
Swedish Research Council (VR)

2015–2017

Hilbert modules of analytic function spaces

Genkai Zhang Analysis and Probability Theory
The Royal Swedish Academy of Science

2013–2016

Analysis on symmetric and locally symmetric spaces. Representations of Lie groups.

Genkai Zhang Analysis and Probability Theory
Swedish Research Council (VR)

There might be more projects where Genkai Zhang participates, but you have to be logged in as a Chalmers employee to see them.

Publications

2017

Eichler-Shimura isomorphism for complex hyperbolic lattices

Inkang Kim, Genkai Zhang
Journal of Geometry and Physics. Vol. 121, p. 452-460
Journal article
2017

TOEPLITZ OPERATORS ON HIGHER CAUCHY-RIEMANN SPACES

M. Englis, Genkai Zhang
Documenta Mathematica. Vol. 22, p. 1081-1116
Journal article
2017

The Capelli Identity and Radon Transform for Grassmannians

S. Sahi, Genkai Zhang
International Mathematics Research Notices (12), p. 3774-3800
Journal article
2017

Tensor products of complementary series of rank one Lie groups

Genkai Zhang
Science China Mathematics. Vol. 60 (11), p. 2337-2348
Journal article
2017

Kahler metric on the space of convex real projective structures on surface

Inkang Kim, Genkai Zhang
Journal of Logic and Computation. Vol. 106 (1), p. 127-137
Journal article
2016

Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups

B. Speh, Genkai Zhang
Mathematische Zeitschrift. Vol. 283 (1-2), p. 629-647
Journal article
2016

Hankel operators and the Dixmier trace on the Hardy space

M. Englis, Genkai Zhang
Journal of the London Mathematical Society. Vol. 94 (2), p. 337-356
Journal article
2016

Invariant Differential Operators on H-Type Groups and Discrete Components in Restrictions of Complementary Series of Rank One Semisimple Groups

Genkai Zhang, B Orsted, Genkai Zhang
Journal of Geometric Analysis. Vol. 26 (1), p. 118-142
Journal article
2016

On boundary value problems for some conformally invariant differential operators

Genkai Zhang, B Orsted, Genkai Zhang
Communications in Partial Differential Equations. Vol. 41 (4), p. 609-643
Journal article
2015

Discrete components in restriction of unitary representations of rank one semisimple Lie groups

Genkai Zhang
Journal of Functional Analysis. Vol. 269 (12), p. 3689-3713
Journal article
2015

Degenerate principal series representations of SO(p+1, p)

V. Fischer, Genkai Zhang
Monatshefte für Mathematik. Vol. 176 (1), p. 87-105
Journal article
2014

Invariant trilinear forms on spherical principal series of real rank one semisimple Lie groups

S. Ben Said, K. Koufany, Genkai Zhang
International Journal of Mathematics. Vol. 25 (3), p. artikel nr 1450017-
Journal article
2013

Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc

G. Misra, S. S. Roy, Genkai Zhang
Proceedings of the American Mathematical Society. Vol. 141 (7), p. 2361-2370
Journal article
2012

Hua operators, Poisson transform and relative discrete series on line bundles over bounded symmetric domains

K. Koufany, Genkai Zhang
Journal of Functional Analysis. Vol. 262 (9), p. 4140-4159
Journal article
2012

Trace formulas and $p$-essentially normal properties of quotient modules on the bidisk

K. Y. Guo, K. Wang, Genkai Zhang
Journal of Operator Theory. Vol. 67 (2), p. 511-535
Journal article
2012

Realization of quaternionic discrete series on the unit ball in H^d

Heping Liu, Genkai Zhang
Journal of Functional Analysis. Vol. 262 (7), p. 2979-3005
Journal article
2011

Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups

Y. Y. Jin, Genkai Zhang
Canadian Mathematical Bulletin. Vol. 54 (1), p. 126-140
Journal article
2010

Ramadanov conjecture and line bundles over compact Hermitian symmetric spaces

M. Englis, Genkai Zhang
Mathematische Zeitschrift. Vol. 264 (4), p. 901-912
Journal article
2010

Rankin–Cohen brackets, transvectants and covariant differential operators

Genkai Zhang
Mathematische Zeitschrift. Vol. 264 (3), p. 513-519
Journal article
2010

Degenerate $p$-Laplacian Operators and Hardy Type Inequalities on H-Type Groups

Y. Y. Jin, Genkai Zhang
Canadian Journal of Mathematics. Vol. 62 (5), p. 1116-1130
Journal article
2010

Degenerate principal series representations and their holomorphic extensions

Genkai Zhang
Advances in Mathematics. Vol. 223 (5), p. 1495-1520
Journal article
2010

Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains

M. Englis, Genkai Zhang
Documenta Mathematica. Vol. 15, p. 601-622
Journal article
2009

Toeplitz and Hankel operators and Dixmier traces on the unit ball of Cn

M. Englis, K. Y. Guo, Genkai Zhang
Proceedings of the American Mathematical Society. Vol. 137 (11), p. 3669-3678
Journal article
2009

Radon, cosine and sine transforms on Grassmannian manifolds.

Genkai Zhang
International Mathematics Research Notices (10), p. 1743-1772
Journal article
2009

Segal–Bargmann and Weyl transforms on compact Lie groups. (With Joachim Hilgert)

J. Hilgert, Genkai Zhang
Monatshefte für Mathematik. Vol. 158 (3), p. 285-305
Journal article
2009

Radon transform on symmetric matrix domains

Genkai Zhang
Transactions of the American Mathematical Society. Vol. 361 (3), p. 1351-1369
Journal article
2007

Radon transform on H-type and siegel-type nilpotent groups

L. Peng, Genkai Zhang
International Journal of Mathematics. Vol. 18 (9), p. 1061-1070
Journal article
2007

Biorthogonal Expansion of Non-Symmetric Jack Functions

Genkai Zhang, S Sahi
SIGMA. Vol. 3, p. 9pp-
Journal article
2007

Radon transform on H-type and Siegel-type nilpotent groups

Genkai Zhang, L. Peng
International Journal of Mathematics. Vol. 18 (9), p. 1061-1070
Journal article
2007

Radon transform on real, complex, and quaternionic Grassmannians.

Genkai Zhang
Duke Mathematical Journal. Vol. 138 (1), p. 137-160
Journal article
2006

Hua operators and Poisson transform for bounded symmetric domains.

Genkai Zhang, K. Koufany
J. Funct. Anal.. Vol. 236 (2), p. 546--580.-
Journal article
2006

Hua operators and Poisson transform for bounded symmetric domains

K. Koufany, Genkai Zhang
Journal of Functional Analysis. Vol. 236 (2), p. 546-580
Journal article
2006

Nonsymmetric Jacobi and Wilson-type polynomials.

Genkai Zhang, L. Peng
Journal article
2006

On the derivatives of the Berezin transform

M. Englis, Genkai Zhang
Proceedings of the American Mathematical Society. Vol. 134 (8), p. 2285-2294
Journal article
2006

Nonsymmetric Jacobi and Wilson-type polynomials

L. Peng, Genkai Zhang
International Mathematics Research Notices
Journal article
2005

Spherical transform and Jacobi polynomials on root systems of type BC

Genkai Zhang
Int. Math. Res. Not.. Vol. 2005 (51), p. 3169--3189.-
Journal article
2005

Laplacians on quotients of Cauchy-Riemann complexes and Szegö map for L2-harmonic forms.

Bent Orsted, Genkai Zhang
Indag. Math. (N.S.). Vol. 16 (3-4), p. 639--653.-
Journal article
2005

Covariant q-differential operators and unitary highest weight representations for U(q)su(n,)n

Dmitry Shklyarov, Genkai Zhang
Journal of Mathematical Physics. Vol. 46 (6), p. 24pp-
Journal article
2004

Hilbert Spaces of tensor-valued holomorphic functions on the unit ball of C-n

S Hwang, Y Liu, Genkai Zhang
Pacific Journal of Mathematics. Vol. 214 (2), p. 303-322
Journal article
2004

Tensor products of holomorphic representations and bilinear differential operators.

L. Peng, Genkai Zhang
Journal of Functional Analysis. Vol. 210 (1), p. 171--192. -
Journal article
2004

On the Faraut-Koranyi hypergeometric functions in rank two.

M. Englis, Genkai Zhang
Ann. Inst. Fourier (Grenoble). Vol. 54 (6), p. 1855--1875-
Journal article
2001

Homogeneous multiplication operators on bounded symmetric domains

Jonathan Arazy, Genkai Zhang
Preprint