DIFFERENTIAL EQUATIONS AND INTERTWINING OPERATORS

Differential equations and intertwining operators

We show that if every module W for a vertex operator algebra V = ∐ n∈Z V(n) satisfies the condition dimW/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 exi...

INTERTWINING DIFFERENTIAL OPERATORS FOR Mp ( « , R ) AND

For each of the two series of groups, three series of representations U„, D„, and H„ (n e Z) are considered. For each series of representations there is a differential operator with the property, that raised to the nth power (n > 0), it intertwines the representations indexed by — n and n. The operators are generalizations of the d'Alembertian, the Diracoperator and a combination of the two. Un...

Intertwining Operators and Residues

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...

Functional Equations Satisfied by Intertwining Operators of Reductive Groups

This paper generalizes a recent work of Vogan and Wallach [VW] in which they derived a difference equation satisfied by intertwining operators of reductive groups. We show that, associated with each irreducible finitedimensional representation, there is a functional equation relating intertwining operators. In this way, we obtain natural relations between intertwining operators for different se...