STAR réprésentations induites

Abstract : This workis devoted to the description of some induced representation series of a Lie group in terms of deformations on some algebras of functions on the associated coadjoint orbits, according to F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D.Sternheimer. The way used is the construction of a symbolic calculous (generalized Weyl transform) on coadjoint orbits and this construction has been realized here in two important cases : the case of the coadjoint orbits of a semi simple Lie group associated to its unitary principal series and the case of massive coadjoint orbits of a generalized Poincaré group (semi direct product of a semi simple Lie group by a vector space). In these two cases, we have defined the star representations (in the Fronsdal's sense associated to the considered representations)
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Benjamin Cahen. STAR réprésentations induites. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1992. Français. ⟨NNT : 1992METZ025S⟩. ⟨tel-01775986⟩

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