INTERTWINING OPERATORS OF THE HEISENBERG GROUP

Singular Convolution Operators on the Heisenberg Group

1. Statement of results and outline of method. The purpose of this note is to announce results dealing with convolution operators on the Heisenberg group. As opposed to the well-known situation where the kernels are homogeneous and C°° away from the origin, the kernels we study are homogeneous but have singularities on a hyperplane. Convolution operators with such kernels arise in the study of ...

Weyl Group Representations and Signatures of Intertwining Operators

For G real split, I studied the (non)-unitarity of a spherical principal series I(1, ν) of G by means of Weyl group representations. For a good choice of the parameter ν, the spherical principal series I(1, ν) admits an invariant hermitian form. To discuss the unitarity of I(1, ν), one needs to compute the signature of such a form. Computations can be done separately on the isotypic of each K−t...

Intertwining Operators and Residues

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...

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 ...