A note on Howe's oscillator semigroup
Annales de l'Institut Fourier, Tome 39 (1989) no. 3, pp. 663-688.

Brunet, Kramer et Howe ont établi l’existence des continuations analytiques pour la représentation métaplectique par des semigroupes d’opérateurs intégraux dans L 2 ( n ) (voir [Howe, Proc. Symp. Pure Math., 48 (1988)] et dans l’espace de Fock (voir [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]). Dans cet article on démontre que les deux semigroupes sont isomorphes et on détermine l’opérateur d’entrelacement.

Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the L 2 ( n ) and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.

     author = {Hilgert, Joachim},
     title = {A note on {Howe's} oscillator semigroup},
     journal = {Annales de l'Institut Fourier},
     pages = {663--688},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {39},
     number = {3},
     year = {1989},
     doi = {10.5802/aif.1182},
     zbl = {0674.47029},
     mrnumber = {91b:22008},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1182/}
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Hilgert, Joachim. A note on Howe's oscillator semigroup. Annales de l'Institut Fourier, Tome 39 (1989) no. 3, pp. 663-688. doi : 10.5802/aif.1182. http://www.numdam.org/articles/10.5802/aif.1182/

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