The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators

The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators

Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for ŝl(2) satisfy certain classical recursion formulas of Rogers and Selberg. These recursions were exploited by Andrews in connection with Gordon’s generalization of the Rogers–Ramanujan identities and with Andrews’ related ide...

Intertwining Operators and Residues

Logarithmic Intertwining Operators and Vertex Operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1)a, of central charge 1 − 12a . We classify these operators in terms of depth and provide explicit constructions ...

Traces of intertwining operators and

Traces of intertwining operators and Macdonald's polynomials Alexander A. Kirillov, Jr. May 1995 Let : V ! V U be an intertwining operator between representations of a simple Lie algebra (quantum group, a ne Lie algebra). We de ne its generalized character to be the following function on the Cartan subalgebra with values in U : (h) = TrV ( eh). This is a generalization of usual characters. Thes...

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...