
Journal of Lie Theory 33 (2023), No. 1, 253270 Copyright Heldermann Verlag 2023 Generalized Laguerre Functions and Whittaker Vectors for Holomorphic Discrete Series Jan Frahm Dept. of Mathematics, Aarhus University, Denmark frahm@math.au.dk Bent Oersted Dept. of Mathematics, Aarhus University, Denmark orsted@math.au.dk Gestur Olafsson Department of Mathematics, Louisiana State University, Baton Rouge, U.S.A. olafsson@math.lsu.edu 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 Ktype expansions. The coefficients are expressed in terms of the generalized Laguerre functions on the corresponding symmetric cone, and we relate the Ktype expansions to the formula for the generating function of the Laguerre polynomials and to their recurrence relations. Keywords: Laguerre functions, Whittaker vectors, holomorphic discrete series. MSC: 22E46; 43A85. [ Fulltextpdf (164 KB)] for subscribers only. 