Relative discrete series of line bundles over bounded symmetric domains

Dooley, Anthony H.; Ørsted, Bent; Zhang, Genkai

Annales de l'Institut Fourier, Tome 46 (1996) no. 4, pp. 1011-1026.

Cet article est une étude de la série relative discrète de l’espace des sections $L^2$ d’un fibré sur un domaine symétrique borné. On démontre que toute série discrète provient, en tant que sous-module irréductible, d’un produit tensoriel d’une série holomorphe discrète par une représentation de dimension finie.

We study the relative discrete series of the $L^2$-space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.

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