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The multiplicity function on exponential and completely solvable homogeneous spaces

✍ Scribed by Ronald L. Lipsman

Publisher
Springer
Year
1991
Tongue
English
Weight
308 KB
Volume
39
Category
Article
ISSN
0046-5755

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✦ Synopsis

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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For a solvable Lie group G the surjectivity of the exponential function expc is equivalent to the connectedness of the near-Cartan subgroups and to the connectedness of the centralizers in a Cartan subgroup of all nilpotent elements in its Lie algebra g. Furthermore, these conditions are satisfied i