Intertwining operators and unitary representations, I

Induced Representations, Intertwining Operators and Transfer

Induced representations and intertwining operators give rise to distributions that represent critical terms in the trace formula. We shall describe a conjectural relationship between these distributions and the LanglandsShelstad-Kottwitz transfer of functions Our goal is to describe a conjectural relationship between intertwining operators and the transfer of functions. One side of the proposed...

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 for Representations Induced from a Maximal Parabolic Subgroup

We present a new method of calculating intertwining operators between principal series representations of semisimple Lie groups G. Working in the compact realization we nd the eigenvalues of the operators on the K-types, and give several examples. Among the advantages of our method is its applicability to bundle-valued cases. 0. Introduction Intertwining operators of various forms play an impor...

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 ...