Geodesic
Generalized Laguerre Functions and Whittaker Vectors for Holomorphic Discrete Series
Journal of Lie theory, Tome 33 (2023) no. 1, pp. 253-27
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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.
Classification : 22E46, 43A85
Mots-clés : Laguerre functions, Whittaker vectors, holomorphic discrete series 
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     author = {J. Frahm and B. Oersted and G. Olafsson},
     title = {Generalized {Laguerre} {Functions} and {Whittaker} {Vectors} for {Holomorphic} {Discrete} {Series}},
     journal = {Journal of Lie theory},
     pages = {253--27},
     year = {2023},
     volume = {33},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2023_33_1_JLT_2023_33_1_a10/}
}
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J. Frahm; B. Oersted; G. Olafsson. Generalized Laguerre Functions and Whittaker Vectors for Holomorphic Discrete Series. Journal of Lie theory, Tome 33 (2023) no. 1, pp. 253-27. http://geodesic.mathdoc.fr/item/JLT_2023_33_1_JLT_2023_33_1_a10/