On the space of $ K$-finite solutions to intertwining differential operators

Toshihisa Kubo*, Bent Orsted

*Corresponding author af dette arbejde

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Abstract

In this paper we give Peter-Weyl-type decomposition theorems for the space of K-finite solutions to intertwining differential operators between parabolically induced representations. Our results generalize a result of Kable for conformally invariant systems. The main idea is based on the duality theorem between intertwining differential operators and homomorphisms between generalized Verma modules. As an application we uniformly realize on the solution spaces of intertwining differential operators all small representations of (SL) over tilde (3,R) attached to the minimal nilpotent orbit.

OriginalsprogEngelsk
TidsskriftRepresentation Theory
Vol/bind23
Nummer7
Sider (fra-til)213-248
Antal sider36
ISSN1088-4165
DOI
StatusUdgivet - sep. 2019

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