Generalized Laguerre Functions and Whittaker Vectors for Holomorphic Discrete Series

J. Frahm; B. Oersted; G. Olafsson

doi:10.5802/jolt.1282

J. Frahm; B. Oersted; G. Olafsson

Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 253-270

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.

arXiv Zbl

DOI: 10.5802/jolt.1282

Classification: 22E46, 43A85
Keywords: 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--270},
     year = {2023},
     volume = {33},
     number = {1},
     doi = {10.5802/jolt.1282},
     zbl = {1552.22049},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1282/}
}

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J. Frahm; B. Oersted; G. Olafsson. Generalized Laguerre Functions and Whittaker Vectors for Holomorphic Discrete Series. Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 253-270. doi: 10.5802/jolt.1282

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