Orbit structure of a distinguished Stein invariant domain in the complexification of a Hermitian symmetric space

2014 ◽  
Vol 278 (3-4) ◽  
pp. 769-793 ◽  
Author(s):  
L. Geatti ◽  
A. Iannuzzi
Keyword(s):  
Symmetric Space ◽  
Hermitian Symmetric Space ◽  
Invariant Domain ◽  
Orbit Structure

scholarly journals Invariant plurisubharmonic functions on non-compact Hermitian symmetric spaces

2021 ◽  
Author(s):  
Laura Geatti ◽  
Andrea Iannuzzi
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Hermitian Symmetric Space ◽  
Hermitian Symmetric Spaces ◽  
Plurisubharmonic Functions ◽  
Invariant Domain ◽  
Compact Hermitian Symmetric Space ◽  
Invariant Domains

AbstractLet $$\,G/K\,$$ G / K be an irreducible non-compact Hermitian symmetric space and let $$\,D\,$$ D be a $$\,K$$ K -invariant domain in $$\,G/K$$ G / K . In this paper we characterize several classes of $$\,K$$ K -invariant plurisubharmonic functions on $$\,D\,$$ D in terms of their restrictions to a slice intersecting all $$\,K$$ K -orbits. As applications we show that $$\,K$$ K -invariant plurisubharmonic functions on $$\,D\,$$ D are necessarily continuous and we reproduce the classification of Stein $$\,K$$ K -invariant domains in $$\,G/K\,$$ G / K obtained by Bedford and Dadok. (J Geom Anal 1:1–17, 1991).

scholarly journals Integrable systems with unitary invariance from non-stretching geometric curve flows in the Hermitian symmetric space Sp(n)/U(n)

2015 ◽  
Vol 38 ◽  
pp. 1560071 ◽  
Author(s):  
Stephen C. Anco ◽  
Esmaeel Asadi ◽  
Asieh Dogonchi
Keyword(s):  
Symmetric Space ◽  
Integrable Systems ◽  
Hermitian Symmetric Space ◽  
Complex Matrix ◽  
Curve Flows ◽  
Frame Method ◽  
Parallel Frame ◽  
Natural Way ◽  
Sg Equation ◽  
Unitary Invariance

A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified Korteweg-de Vries equation and a Hamiltonian sine-Gordon (SG) equation, involving a scalar variable coupled to a complex vector variable. The Hermitian structure of the symmetric space Sp(n)/U(n) is used in a natural way from the beginning in formulating a complex matrix representation of the tangent space 𝔰𝔭(n)/𝔲(n) and its bracket relations within the symmetric Lie algebra (𝔲(n), 𝔰𝔭(n)).

scholarly journals Hermitian symmetric space, flat bundle and holomorphicity criterion

2016 ◽  
Vol 140 (4) ◽  
pp. 1-10
Author(s):  
Hassan Azad ◽  
Indranil Biswas ◽  
C.S. Rajan ◽  
Shehryar Sikander
Keyword(s):  
Symmetric Space ◽  
Hermitian Symmetric Space ◽  
Flat Bundle

scholarly journals Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace

1997 ◽  
Vol 12 (34) ◽  
pp. 2623-2630 ◽  
Author(s):  
H. Aratyn ◽  
C. Rasinariu ◽  
A. Das
Keyword(s):  
Symmetric Space ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Space Structure ◽  
Hermitian Symmetric Space ◽  
Curvature Condition ◽  
Lax Equation ◽  
Abelian Gauge ◽  
Graded Algebras ◽  
Zero Curvature

We generalize the Drinfeld–Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl (n+1,n), providing the Hermitian symmetric space structure.

Higher-order solutions of a matrix AKNS system associated with a Hermitian symmetric space

2019 ◽  
Vol 383 (25) ◽  
pp. 3047-3055 ◽  
Author(s):  
Xianguo Geng ◽  
Jing Shen ◽  
Bo Xue
Keyword(s):  
Symmetric Space ◽  
Higher Order ◽  
Hermitian Symmetric Space ◽  
Akns System

The projective rank of a Hermitian symmetric space: A geometric approach and consequences

2002 ◽  
Vol 323 (2) ◽  
pp. 351-375
Author(s):  
Cristián U. Sánchez ◽  
Ana Giunta
Keyword(s):  
Symmetric Space ◽  
Geometric Approach ◽  
Hermitian Symmetric Space
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