# Institut for Matematik

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

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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.

Originalsprog Engelsk Representation Theory 23 213-248 36 1088-4165 https://doi.org/10.1090/ert/527 Udgivet - sep. 2019

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