Verma Modules Over the Generalized Heisenberg–Virasoro Algebra

Verma modules over the generalized Heisenberg-Virasoro algebra

For any additive subgroup G of an arbitrary field F of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra L[G]. Given a total order of G compatible with its group structure, and any h, hI , c, cI , cLI ∈ F, a Verma module M̃(h, hI , c, cI , cLI) over L[G] is defined. In the this note, the irreducibility of Verma modules M̃(h, hI , c, cI , cLI) is completely determined.

Generalized Verma Modules

R – Conformal Symmetries . Ii . Geometric Quantization and Hidden Symmetries of Verma Modules over Virasoro Algebra

This article being a continuation of the first part [1] is addressed to specialists in representation theory, infinite dimensional geometry, quantum algebra, mathematical physics and informatics of interactive systems. The interrelations of the infinite dimensional geometry of the homogeneous Kähler manifold M = Diff+(S )/S (see e.g. [2] and numerous refs wherein), its quotient M1 = Diff+(S )/P...

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...

Systems of Differential Operators and Generalized Verma Modules

In this paper we close the cases that were left open in our earlier works on the study of conformally invariant systems of second-order differential operators for degenerate principal series. More precisely, for these cases, we find the special values of the systems of differential operators, and determine the standardness of the homomorphisms between the generalized Verma modules, that come fr...