In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important resu...

In this paper, new examples of weakly symmetric spaces in the sense of A. Selberg 14] are constructed. Let G be a connected, simply-connected, simple Lie group of hermitian type and K a maximal compactly embedded subgroup of G such that D = G=K is an irreducible classical bounded symmetric domain. Let G 1 and D 1 be circle extensions of G and D, respectively. The factor of automorphy induces a ...

this research was an attempt to study reasons for creation of some of the important and sacred numbers and their reflection in architectural and urban spaces. this subject matter is important because significant and sacred numbers were used in design and construction of a number of historical spaces. the research objective was to discover some of the reasons for formation of important and sacre...

1. Matrices, Vectors and their Basic Operations 1.1. Matrices 1.2. Vectors 1.3. Addition and Scalar Multiplication of Matrices 1.4. Multiplication of Matrices 2. Determinants 2.1. Square Matrices 2.2. Determinants 2.3. Cofactors and the Inverse Matrix 3. Systems of Linear Equations 3.1. Linear Equations 3.2. Cramer’s Rule 3.3. Eigenvalues of a Complex Square Matrix 3.4. Jordan Canonical Form 4....

We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various classes of solutions to the classical extremal black hole Attractor Equations. Relations with Jordan algebras of degree three and four are also outlined.

This paper is based on a talk given at the conference ”Representation theory of real reductive groups”, Salt Lake City, July 2009. We fix an algebraically closed field k of characteristic exponent p. (We assume, except in §17, that either p = 1 or p ≫ 0.) We also fix a symmetric space that is a triple (G, θ,K) where G is a connected reductive algebraic group over k, θ : G −→ G is an involution ...

We determine explicitly the local structure of a semi-symmetric P-space.

Semiuniform convergence spaces form a common generalization of lter spaces (including symmetric convergence spaces and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform conver...

study on polsar target detection essentially requires the cattering information and polarimetric statistical data. theoretical analysis shows that some terms of the second order scattering matrices such as coherence and covariance matrix clearly show the differences between nonsymmetrical man-made objects and natural clatters which being reflection symmetric. using the model derived from these ...