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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.

Original languageEnglish
JournalRepresentation Theory
Pages (from-to)213-248
Number of pages36
Publication statusPublished - Sep 2019

    Research areas

  • Intertwining differential operators, generalized Verma modules, duality theorem, K-finite solutions, Peter-Weyl-type formulas, small representations, Torasso's representation, hypergeometric polynomials, CONFORMALLY INVARIANT-SYSTEMS, HEISENBERG ULTRAHYPERBOLIC EQUATION, MINIMAL REPRESENTATION, SINGULAR REPRESENTATION, UNITARY REPRESENTATIONS, O(P, SL(3

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