Generalized Laguerre Functions and Whittaker Vectors for Holomorphic Discrete Series

Authors

Jan Frahm, Aarhus Universitet
Gestur Ólafsson, Louisiana State University
Bent Ørsted, Aarhus Universitet

Document Type

Article

Publication Date

1-1-2023

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 L²-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.

Publication Source (Journal or Book title)

Journal of Lie Theory

First Page

253

Last Page

270

Recommended Citation

Frahm, J., Ólafsson, G., & Ørsted, B. (2023). Generalized Laguerre Functions and Whittaker Vectors for Holomorphic Discrete Series. Journal of Lie Theory, 33 (1), 253-270. Retrieved from https://repository.lsu.edu/mathematics_pubs/1615