1. Finite multiplicity theorems for induction and restriction.
- Author
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Kobayashi, Toshiyuki and Oshima, Toshio
- Subjects
- *
MULTIPLICITY (Mathematics) , *FINITE groups , *MATHEMATICAL induction , *REPRESENTATION theory , *FLAG manifolds (Mathematics) , *GEOMETRIC analysis - Abstract
Abstract: We find upper and lower bounds of the multiplicities of irreducible admissible representations π of a semisimple Lie group G occurring in the induced representations from irreducible representations τ of a closed subgroup H. As corollaries, we establish geometric criteria for finiteness of the dimension of (induction) and of (restriction) by means of the real flag variety , and discover that uniform boundedness property of these multiplicities is independent of real forms and characterized by means of the complex flag variety. [Copyright &y& Elsevier]
- Published
- 2013
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