Genkai Zhang

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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 Department of Mathematical Sciences, Mathematics
Swedish Research Council (VR)

2015–2017

Hilbert modules of analytic function spaces

Genkai Zhang Department of Mathematical Sciences, Mathematics
The Royal Swedish Academy of Science

2013–2016

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

Genkai Zhang Department of Mathematical Sciences, Mathematics
Swedish Research Council (VR)

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Publications

2016

Hankel operators and the Dixmier trace on the Hardy space

M. Englis, Genkai Zhang,
Journal of the London Mathematical Society. Vol. 94, p. 337-356
Scientific journal article - peer reviewed
2016

On boundary value problems for some conformally invariant differential operators

J. Mollers, B. Orsted, Genkai Zhang et al
Communications in Partial Differential Equations. Vol. 41 (4), p. 609-643
Scientific journal article - peer reviewed
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
Scientific journal article - peer reviewed
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, J Moellers et al
Journal of Geometric Analysis. Vol. 26 (1), p. 118-142
Scientific journal article - peer reviewed
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
Scientific journal article - peer reviewed
2015

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

V. Fischer, Genkai Zhang,
Monatshefte Fur Mathematik. Vol. 176 (1), p. 87-105
Scientific journal article - peer reviewed
2014

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

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

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

G. Misra, S. S. Roy, Genkai Zhang et al
Proceedings of the American Mathematical Society. Vol. 141 (7), p. 2361-2370
Scientific journal article - peer reviewed
2012

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

K. Y. Guo, K. Wang, Genkai Zhang et al
Journal of Operator Theory. Vol. 67 (2), p. 511-535
Scientific journal article - peer reviewed
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
Scientific journal article - peer reviewed
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
Scientific journal article - peer reviewed
2011

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

Y. Y. Jin, Genkai Zhang,
Canadian Mathematical Bulletin - Bulletin Canadien De Mathematiques. Vol. 54 (1), p. 126-140
Scientific journal article - peer reviewed
2010

Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains

M. Englis, Genkai Zhang,
Documenta Mathematica. Vol. 15, p. 601-622
Scientific journal article - peer reviewed
2010

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

Yongyang Jin, Genkai Zhang,
Canadian Journal of Mathematics. Vol. 62, p. 1116-1130
Scientific journal article - peer reviewed
2010

Rankin–Cohen brackets, transvectants and covariant differential operators

Genkai Zhang,
Mathematische Zeitschrift. Vol. 264 (3), p. 513-519
Scientific journal article - peer reviewed
2010

Ramadanov conjecture and line bundles over compact Hermitian symmetric spaces

M. Englis, Genkai Zhang,
Mathematische Zeitschrift. Vol. 264 (4), p. 901-912
Scientific journal article - peer reviewed
2010

Degenerate principal series representations and their holomorphic extensions

Genkai Zhang,
Advances in Mathematics. Vol. 223 (5), p. 1495-1520
Scientific journal article - peer reviewed
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
Scientific journal article - peer reviewed
2009

Radon, cosine and sine transforms on Grassmannian manifolds.

Genkai Zhang,
International Mathematics Research Notices (10), p. 1743-1772
Scientific journal article - peer reviewed
2009

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

M. Englis, K. Guo, Genkai Zhang et al
Proceedings of the American Mathematical Society. Vol. 137 (11), p. 3669-3678
Scientific journal article - peer reviewed
2009

Radon transform on symmetric matrix domains

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

Biorthogonal Expansion of Non-Symmetric Jack Functions

Genkai Zhang, S Sahi,
SIGMA. Vol. 3, p. 9pp
Scientific journal article - peer reviewed
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
Scientific journal article - peer reviewed
2007

Radon transform on real, complex, and quaternionic Grassmannians.

Genkai Zhang,
Duke Math. J. . Vol. 138 (1), p. 137-160
Scientific journal article - peer reviewed
2006

Nonsymmetric Jacobi and Wilson-type polynomials

L. Peng, Genkai Zhang,
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Scientific journal article - peer reviewed
2006

Hua operators and Poisson transform for bounded symmetric domains

K. Koufany, Genkai Zhang,
JOURNAL OF FUNCTIONAL ANALYSIS. Vol. 236 (2), p. 546-580
Scientific journal article - peer reviewed
2006

On the derivatives of the Berezin transform

M. Englis, Genkai Zhang,
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. Vol. 134 (8), p. 2285-2294
Scientific journal article - peer reviewed
2006

Nonsymmetric Jacobi and Wilson-type polynomials.

Genkai Zhang, L. Peng,
Int. Math. Res. Not.
Scientific journal article - peer reviewed
2006

Hua operators and Poisson transform for bounded symmetric domains.

Genkai Zhang, K. Koufany,
J. Funct. Anal. . Vol. 236 (2), p. 546--580.
Scientific journal article - peer reviewed
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
Scientific journal article - peer reviewed
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.
Scientific journal article - peer reviewed
2005

Spherical transform and Jacobi polynomials on root systems of type BC

Genkai Zhang,
Int. Math. Res. Not. . Vol. 2005 (51), p. 3169--3189.
Scientific journal article - peer reviewed
2004

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

S Hwang, Y Liu, Genkai Zhang et al
PACIFIC JOURNAL OF MATHEMATICS. Vol. 214 (2), p. 303-322
Scientific journal article - peer reviewed
2004

Tensor products of holomorphic representations and bilinear differential operators.

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

On the Faraut-Koranyi hypergeometric functions in rank two.

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

Homogeneous multiplication operators on bounded symmetric domains

Jonathan Arazy, Genkai Zhang,
Preprint