scholarly journals Intertwining operators for solving differential equations, with applications to symmetric spaces

1990 ◽  
Vol 130 (1) ◽  
pp. 61-82 ◽  
Author(s):  
Arlen Anderson ◽  
Roberto Camporesi
Keyword(s):  
Differential Equations ◽  
Symmetric Spaces ◽  
Intertwining Operators

scholarly journals Conformal and Geodesic Mappings onto Some Special Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 664 ◽  
Author(s):  
Volodymyr Berezovski ◽  
Yevhen Cherevko ◽  
Lenka Rýparová
Keyword(s):  
Differential Equations ◽  
Closed System ◽  
Symmetric Spaces ◽  
Conformal Mappings ◽  
Cauchy Type ◽  
Affine Connections ◽  
Covariant Derivatives ◽  
Riemannian Spaces

In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

NONLINEAR SCHRÖDINGER EQUATIONS ON SUPER SYMMETRIC SPACES RELATED TO LIE SUPERALGEBRAS A(m, n)

1991 ◽  
Vol 06 (26) ◽  
pp. 4655-4666 ◽  
Author(s):  
AHMET CANOḠLU ◽  
BAHRİ GÜLDOḠAN ◽  
SELÂMİ SALİHOḠLU
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetric Spaces ◽  
Nonlinear Partial Differential Equations ◽  
Lie Superalgebras ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

We obtain new integrable coupled nonlinear partial differential equations by assuming that the soliton connection has values in the Lie superalgebras A(m, n). These equations are coupled nonlinear Schrödinger equations on various super symmetric spaces.

scholarly journals On Canonical Almost Geodesic Mappings of Type π2(e)

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 54 ◽  
Author(s):  
Volodymyr Berezovski ◽  
Josef Mikeš ◽  
Lenka Rýparová ◽  
Almazbek Sabykanov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetric Spaces ◽  
Riemann Tensor ◽  
Mixed System ◽  
Cauchy Type ◽  
Partial Differential ◽  
Affine Connections

In the paper, we consider canonical almost geodesic mappings of type π 2 ( e ) . We have found the conditions that must be satisfied for the mappings to preserve the Riemann tensor. Furthermore, we consider canonical almost geodesic mappings of type π 2 ( e ) of spaces with affine connections onto symmetric spaces. The main equations for the mappings are obtained as a closed mixed system of Cauchy-type Partial Differential Equations. We have found the maximum number of essential parameters which the solution of the system depends on.

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connection Onto Generalized 2-Ricci-Symmetric Spaces

2021 ◽  
Vol 22 ◽  
pp. 78-87
Author(s):  
Volodymyr Berezovski ◽  
Yevhen Cherevko ◽  
Svitlana Leshchenko ◽  
Josef Mikes
Keyword(s):  
Differential Equations ◽  
Closed System ◽  
Symmetric Spaces ◽  
Affine Connection ◽  
Linear Differential Equations ◽  
Cauchy Type ◽  
Affine Connections ◽  
Covariant Derivatives ◽  
Linear Differential

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces. The main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained result extends an amount of research produced by Sinyukov, Berezovski and Mike\v{s}.

scholarly journals DIFFERENTIAL EQUATIONS AND INTERTWINING OPERATORS

2005 ◽  
Vol 07 (03) ◽  
pp. 375-400 ◽  
Author(s):  
YI-ZHI HUANG
Keyword(s):  
Differential Equations ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Tensor Category ◽  
Extension Property ◽  
Singular Points ◽  
Intertwining Operators ◽  
Natural Structure ◽  
Systems Of Differential Equations

We show that if every module W for a vertex operator algebra V = ∐n∈ℤV(n) satisfies the condition dim W/C1(W)<∞, where C1(W) is the subspace of W spanned by elements of the form u-1w for u ∈ V+ = ∐n>0 V(n) and w ∈ W, then matrix elements of products and iterates of intertwining operators satisfy certain systems of differential equations. Moreover, for prescribed singular points, there exist such systems of differential equations such that the prescribed singular points are regular. The finiteness of the fusion rules is an immediate consequence of a result used to establish the existence of such systems. Using these systems of differential equations and some additional reductivity conditions, we prove that products of intertwining operators for V satisfy the convergence and extension property needed in the tensor product theory for V-modules. Consequently, when a vertex operator algebra V satisfies all the conditions mentioned above, we obtain a natural structure of vertex tensor category (consequently braided tensor category) on the category of V-modules and a natural structure of intertwining operator algebra on the direct sum of all (inequivalent) irreducible V-modules.

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