Abstract
It has been shown recently that the same multiplicity function appears in direct integral decompositions of both induced and restricted representations on exponential solvable groups — that is, a generalized form of Frobenius Reciprocity is valid. Qualitative results on that multiplicity function in the completely solvable case are proven in this paper — namely, necessary and sufficient conditions for finiteness and boundedness are obtained. The proof uses techniques from ‘pseudo-algebraic geometry’.
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Research supported by DMS 87-00551A02.
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Lipsman, R.L. The multiplicity function on exponential and completely solvable homogeneous spaces. Geom Dedicata 39, 155–161 (1991). https://doi.org/10.1007/BF00182291
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DOI: https://doi.org/10.1007/BF00182291