On the Rigidity of Differential Systems modelled on Hermitian Symmetric Spaces and Disproofs of a Conjecture concerning Modular Interpretations of Configuration Spaces

2018 ◽  
Author(s):  
Takeshi Sasaki ◽  
Keizo Yamaguchi ◽  
Masaaki Yoshida
Keyword(s):  
Symmetric Spaces ◽  
Configuration Spaces ◽  
Hermitian Symmetric Spaces ◽  
Differential Systems

scholarly journals Differential systems of type (1,1) on Hermitian symmetric spaces and their solutions

2004 ◽  
Vol 215 (2) ◽  
pp. 427-475
Author(s):  
C Benson ◽  
D Buraczewski ◽  
E Damek ◽  
G Ratcliff
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces ◽  
Differential Systems

scholarly journals ON MATRIX KP AND SUPER-KP HIERARCHIES IN THE HOMOGENEOUS GRADING

1996 ◽  
Vol 11 (18) ◽  
pp. 3257-3295 ◽  
Author(s):  
F. TOPPAN
Keyword(s):  
Power Series ◽  
Symmetric Spaces ◽  
Unexpected Result ◽  
Hermitian Symmetric Spaces ◽  
Regular Elements ◽  
Symmetry Properties ◽  
Alternating Sums ◽  
Spectral Parameter Power Series ◽  
Special Limit ◽  
Free Parameters

Constrained KP and super-KP hierarchies of integrable equations (generalized NLS hierarchies) are systematically produced through a Lie-algebraic AKS matrix framework associated with the homogeneous grading. The role played by different regular elements in defining the corresponding hierarchies is analyzed, as well as the symmetry properties under the Weyl group transformations. The coset structure of higher order Hamiltonian densities is proven. For a generic Lie algebra the hierarchies considered here are integrable and essentially dependent on continuous free parameters. The bosonic hierarchies studied in Refs. 1 and 2 are obtained as special limit restrictions on Hermitian symmetric spaces. In the supersymmetric case the homogeneous grading is introduced consistently by using alternating sums of bosons and fermions in the spectral parameter power series. The bosonic hierarchies obtained from [Formula: see text] and the supersymmetric ones derived from the N=1 affinization of sl (2), sl (3) and osp (1|2) are explicitly constructed. An unexpected result is found: only a restricted subclass of the sl (3) bosonic hierarchies can be supersymmetrically extended while preserving integrability.

Hyperkähler Metrics on Cotangent Bundles of Hermitian Symmetric Spaces

2021 ◽  
pp. 287-298
Author(s):  
Olivier Biquard ◽  
Paul Gauduchon
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces ◽  
Cotangent Bundles ◽  
Hyperkähler Metrics

Berezin Quantization on Para-Hermitian Symmetric Spaces

2012 ◽  
pp. 71-80
Author(s):  
Vladimir F. Molchanov
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces ◽  
Berezin Quantization

Coupled Vortex Equations on Complete Kähler Manifolds

2008 ◽  
Vol 51 (3) ◽  
pp. 467-480
Author(s):  
Yue Wang
Keyword(s):  
Symmetric Spaces ◽  
Existence Results ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Convex Domains ◽  
Hermitian Symmetric Spaces ◽  
Vortex Equations ◽  
Curved Manifolds ◽  
Pseudo Convex ◽  
Simply Connected

AbstractIn this paper, we first investigate the Dirichlet problem for coupled vortex equations. Secondly, we give existence results for solutions of the coupled vortex equations on a class of complete noncompact Kähler manifolds which include simply-connected strictly negative curved manifolds, Hermitian symmetric spaces of noncompact type and strictly pseudo-convex domains equipped with the Bergmann metric.

On Heisenberg models with values in Hermitian symmetric spaces

1985 ◽  
Vol 9 (2) ◽  
pp. 107-112 ◽  
Author(s):  
Yoshimasa Nakamura
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces ◽  
Heisenberg Models

scholarly journals Minimal symplectic atlases of Hermitian symmetric spaces

2015 ◽  
Vol 85 (1) ◽  
pp. 79-85
Author(s):  
Roberto Mossa ◽  
Giovanni Placini
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces
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