On the real points of an arithmetic quotient of a bounded symmetric domain

1975 ◽  
Vol 215 (2) ◽  
pp. 135-164 ◽  
Author(s):  
Goro Shimura
Keyword(s):  
Symmetric Domain ◽  
Bounded Symmetric Domain ◽  
The Real ◽  
Arithmetic Quotient

scholarly journals REGULAR FUNCTIONS ON THE SHILOV BOUNDARY

2005 ◽  
Vol 04 (06) ◽  
pp. 613-629 ◽  
Author(s):  
OLGA BERSHTEIN
Keyword(s):  
Symmetric Domain ◽  
Principal Series ◽  
Bounded Symmetric Domain ◽  
Bounded Symmetric Domains ◽  
Shilov Boundary ◽  
Generators And Relations ◽  
Regular Functions ◽  
Degenerate Principal Series

In this paper a *-algebra of regular functions on the Shilov boundary S(𝔻) of bounded symmetric domain 𝔻 is constructed. The algebras of regular functions on S(𝔻) are described in terms of generators and relations for two particular series of bounded symmetric domains. Also, the degenerate principal series of quantum Harish–Chandra modules related to S(𝔻) = Un is investigated.

Bloch Space of a Bounded Symmetric Domain and Composition Operators

2018 ◽  
Vol 13 (2) ◽  
pp. 479-492 ◽  
Author(s):  
Cho-Ho Chu ◽  
Hidetaka Hamada ◽  
Tatsuhiro Honda ◽  
Gabriela Kohr
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Symmetric Domain ◽  
Bounded Symmetric Domain

scholarly journals Dynamics of Biholomorphic Self-Maps on Bounded Symmetric Domains

2015 ◽  
Vol 117 (2) ◽  
pp. 203 ◽  
Author(s):  
P. Mellon
Keyword(s):  
Fixed Point ◽  
Boundary Component ◽  
Symmetric Domain ◽  
Bounded Symmetric Domain ◽  
Bounded Symmetric Domains ◽  
Linear Isometry ◽  
Holomorphic Map ◽  
Infinite Dimensional ◽  
Hilbert Ball

Let $g$ be a fixed-point free biholomorphic self-map of a bounded symmetric domain $B$. It is known that the sequence of iterates $(g^n)$ may not always converge locally uniformly on $B$ even, for example, if $B$ is an infinite dimensional Hilbert ball. However, $g=g_a\circ T$, for a linear isometry $T$, $a=g(0)$ and a transvection $g_a$, and we show that it is possible to determine the dynamics of $g_a$. We prove that the sequence of iterates $(g_a^n)$ converges locally uniformly on $B$ if, and only if, $a$ is regular, in which case, the limit is a holomorphic map of $B$ onto a boundary component (surprisingly though, generally not the boundary component of $\frac{a}{\|a\|}$). We prove $(g_a^n)$ converges to a constant for all non-zero $a$ if, and only if, $B$ is a complex Hilbert ball. The results are new even in finite dimensions where every element is regular.

scholarly journals Symmetry and Special Relativity

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1235 ◽  
Author(s):  
Yaakov Friedman ◽  
Tzvi Scarr
Keyword(s):  
Charged Particle ◽  
Special Relativity ◽  
Symmetric Domain ◽  
Analytic Solutions ◽  
Bounded Symmetric Domain ◽  
Speed Of Light ◽  
Conformal Maps ◽  
Principle Of Relativity ◽  
Electric And Magnetic Fields ◽  
Inertial Frames

We explore the role of symmetry in the theory of Special Relativity. Using the symmetry of the principle of relativity and eliminating the Galilean transformations, we obtain a universally preserved speed and an invariant metric, without assuming the constancy of the speed of light. We also obtain the spacetime transformations between inertial frames depending on this speed. From experimental evidence, this universally preserved speed is c, the speed of light, and the transformations are the usual Lorentz transformations. The ball of relativistically admissible velocities is a bounded symmetric domain with respect to the group of affine automorphisms. The generators of velocity addition lead to a relativistic dynamics equation. To obtain explicit solutions for the important case of the motion of a charged particle in constant, uniform, and perpendicular electric and magnetic fields, one can take advantage of an additional symmetry—the symmetric velocities. The corresponding bounded domain is symmetric with respect to the conformal maps. This leads to explicit analytic solutions for the motion of the charged particle.

Bergman–Hartogs domains and their automorphisms

2019 ◽  
pp. 316-323
Author(s):  
Guy ROOS
Keyword(s):  
Automorphism Groups ◽  
Symmetric Domain ◽  
Bounded Symmetric Domain ◽  
Homogeneous Domain ◽  
Hartogs Domains ◽  
Bounded Homogeneous Domain

For Cartan–Hartogs domains and also for Bergman–Hartogs domains, the determination of their automorphism groups is given for the cases when the base is any bounded symmetric domain and a general bounded homogeneous domain respectively.

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