Generalized Laguerre functions and Whittaker vectors for holomorphic discrete series

Jan Frahm, Bent Ørsted, Gestur Ólafsson

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Abstract

We study degenerate Whittaker vectors in scalar type holomorphic discrete series representations of tube type Hermitian Lie groups and their analytic continuation. In four different realizations, the bounded domain picture, the tube domain picture, the $L^2$-model and the Fock model, we find their explicit $K$-type expansions. The coefficients are expressed in terms of the generalized Laguerre functions on the corresponding symmetric cone, and we relate the $K$-type expansions to the formula for the generating function of the Laguerre polynomials and to their recurrence relations.
OriginalsprogEngelsk
TidsskriftJournal of Lie Theory
Vol/bind33
Nummer1
Sider (fra-til)253-270
Antal sider18
ISSN0949-5932
StatusUdgivet - 2023
  • Symmetry Breaking in Mathematics

    Frahm, J., Weiske, C., Ditlevsen, J., Spilioti, P., Bang-Jensen, F. J. & Labriet, Q.

    01/08/201931/07/2024

    Projekter: ProjektForskning

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