Genkai Zhang
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 in
Europe, China, Japan, South Korea and USA.
Showing 71 publications
Cartan–Helgason theorem for quaternionic symmetric and twistor spaces
Weighted Bergman kernels for nearly holomorphic functions on bounded symmetric domains
Casimir energy of hyperbolic orbifolds with conical singularities
Convexity of energy functions of harmonic maps homotopic to covering maps of surfaces
Wehrl-Type Inequalities for Bergman Spaces on Domains in C<sup>d</sup> and Completely Positive Maps
Plurisubharmonicity and Geodesic Convexity of Energy Function on Teichmuller Space
Principal series of Hermitian Lie groups induced from Heisenberg parabolic subgroups
BRANCHING OF METAPLECTIC REPRESENTATION OF Sp(2,R) UNDER ITS PRINCIPAL SL(2,R)-SUBGROUP
Second variation of Selberg zeta functions and curvature asymptotics
An extension problem related to the fractional Branson–Gover operators
Plurisuperharmonicity of reciprocal energy function on Teichmüller space and Weil-Petersson metric
Toledo invariant of lattices in SU(2,1) via symmetric square
CONNECTION AND CURVATURE ON BUNDLES OF BERGMAN AND HARDY SPACES
Hausdorff Moment Sequences Induced by Rational Functions
Holomorphic Isometries from the Unit Ball into Symmetric Domains
Positivity of Shimura operators
Local rigidity of complex hyperbolic lattices in semisimple Lie groups
Convex real projective structures and Weil's local rigidity theorem
The Capelli Identity and Radon Transform for Grassmannians
Eichler-Shimura isomorphism for complex hyperbolic lattices
Curvature inequalities for operators of the Cowen-Douglas class
Kahler metric on the space of convex real projective structures on surface
Tensor products of complementary series of rank one Lie groups
TOEPLITZ OPERATORS ON HIGHER CAUCHY-RIEMANN SPACES
Hankel operators and the Dixmier trace on the Hardy space
On boundary value problems for some conformally invariant differential operators
Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups
Discrete components in restriction of unitary representations of rank one semisimple Lie groups
Degenerate principal series representations of SO(p+1, p)
Invariant trilinear forms on spherical principal series of real rank one semisimple Lie groups
Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc
Trace formulas and $p$-essentially normal properties of quotient modules on the bidisk
Realization of quaternionic discrete series on the unit ball in H^d
Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups
Degenerate $p$-Laplacian Operators and Hardy Type Inequalities on H-Type Groups
Ramadanov conjecture and line bundles over compact Hermitian symmetric spaces
Rankin–Cohen brackets, transvectants and covariant differential operators
Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains
Degenerate principal series representations and their holomorphic extensions
Radon transform on symmetric matrix domains
Radon, cosine and sine transforms on Grassmannian manifolds.
Segal–Bargmann and Weyl transforms on compact Lie groups. (With Joachim Hilgert)
Toeplitz and Hankel operators and Dixmier traces on the unit ball of Cn
Radon transform on real, complex, and quaternionic Grassmannians.
Radon transform on H-type and siegel-type nilpotent groups
Radon transform on H-type and Siegel-type nilpotent groups
Biorthogonal Expansion of Non-Symmetric Jack Functions
Hua operators and Poisson transform for bounded symmetric domains
Hua operators and Poisson transform for bounded symmetric domains.
On the derivatives of the Berezin transform
Nonsymmetric Jacobi and Wilson-type polynomials.
Nonsymmetric Jacobi and Wilson-type polynomials
Covariant q-differential operators and unitary highest weight representations for U(q)su(n,)n
Spherical transform and Jacobi polynomials on root systems of type BC
Laplacians on quotients of Cauchy-Riemann complexes and Szegö map for L2-harmonic forms.
On the Faraut-Koranyi hypergeometric functions in rank two.
Hilbert Spaces of tensor-valued holomorphic functions on the unit ball of C-n
Tensor products of holomorphic representations and bilinear differential operators.
Invariant differential operators on symmetric cones and Hermitian symmetric spaces
Homogeneous multiplication operators on bounded symmetric domains
Branching coefficients of holomorphic representations and Segal-Bargmann transform
Capelli identity and relative discrete series of the line bundle over tube domains
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Showing 4 research projects
Hilbert modules of analytic function spaces
Analysis on symmetric and locally symmetric spaces. Representations of Lie groups.
Radon transform. Harmonic and Complex Analysis on symmetric spaces. Representations of Lie groups.