Geodesic
Harmonic analysis on the infinite-dimensional unitary-symplectic group
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 118-141

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The goal of harmonic analysis on the infinite-dimensional unitary-symplectic group is to decompose a certain family of unitary representations of this group that replace the nonexisting regular representation and depend on a complex parameter. The aim of the present paper is to describe the decomposition for an integer parameter. 
@article{ZNSL_2012_403_a8,
     author = {A. Osinenko},
     title = {Harmonic analysis on the infinite-dimensional unitary-symplectic group},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {118--141},
     publisher = {mathdoc},
     volume = {403},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_403_a8/}
}
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A. Osinenko. Harmonic analysis on the infinite-dimensional unitary-symplectic group. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 118-141. http://geodesic.mathdoc.fr/item/ZNSL_2012_403_a8/