Systems of Differential Operators and Generalized Verma Modules

New Generalized Verma Modules and Multilinear Intertwining Differential Operators

The present paper contains two interrelated developments. First are proposed new generalized Verma modules. They are called k Verma modules, k ∈ IN , and coincide with the usual Verma modules for k = 1. As a vector space a k Verma module is isomorphic to the symmetric tensor product of k copies of the universal enveloping algebra U(G), where G is the subalgebra of lowering generators in the sta...

Dynamical Systems on Hilbert C*-Modules

System of fuzzy fractional differential equations in generalized metric space

In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point princi...

Rough approximation operators based on quantale-valued fuzzy generalized neighborhood systems

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...

Homomorphisms of Semiholonomic Verma Modules: an Exceptional Case

It is well known that Verma module homomorphisms correspond to invariant operators on homogeneous spaces, which in certain situations can be regarded as the flat models of specific differential geometries. This can be generalised to curved space by introducing semiholonomic Verma modules, whose homomorphisms give rise to invariant operators on curved space. In this article we investigate from a...