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Hidénori Fujiwara (2005)
UNE RÉCIPROCITÉ DE FROBENIUS
A. Baklouti, H. Fujiwara, J. Ludwig (2008)
A variant of the Frobenius reciprocity for restricted representations on nilpotent Lie groups
Hidénori Fujiwara (1987)
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L. Corwin, F. Greenleaf (1988)
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Abstract. Soit un groupe de Lie nilpotent d'algèbre de Lie . Soit le dual unitaire de G et prenons une représentation dont l'orbite coadjointe associée se note . Comme la réciprocité de Frobenius le suggère, il existe une sorte de dualité entre l'induction et la restriction de représentations, spécialement dans les formules de désintégration en irréductibles. Soient K un sous-groupe analytique de G et la restriction de à K . Il est bien connu que, selon la géométrie de et la structure de K , la restriction est à multiplicités soit uniformément finies soit uniformément égales à l'infini. Dans ce papier, nous écrivons les formules de Plancherel et de Penney–Plancherel pour la restriction supposée être à multiplicités finies. La méthode des orbites nous est alors très utile pour accomplir cette étude. Let be a nilpotent Lie group with Lie algebra . Let be the unitary dual of G and associated to a coadjoint orbit . As suggested by the Frobenius reciprocity, there is a sort of duality between the induction and the restriction of unitary representations, namely in the disintegration formulae into irreducibles. Let K be an analytic subgroup of G and be the restriction of to K . It is well known, depending upon the geometry of and the structure of K , that the multiplicities of are either uniformly finite or uniformly infinite. In this paper, we write down the Plancherel and the Penney–Plancherel formulae for supposed to be of finite multiplicities. The orbit method turns out to be very useful for our study.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Apr 1, 2013
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