Multiplicity formulas for finite dimensional and generalized principal series representations |
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Authors: | M S Bakre |
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Institution: | (1) Department of Mathematics, University of Bombay, 400 098 Bombay, India |
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Abstract: | The article presents two results. (1) Let a be a reductive Lie algebra over ℂ and let b be a reductive subalgebra of a. The
first result gives the formula for multiplicity with which a finite dimensional irreducible representation of b appears in
a given finite dimensional irreducible representation of a in a general situation. This generalizes a known theorem due to
Kostant in a special case. (2) LetG be a connected real semisimple Lie group andK a maximal compact subgroup ofG. The second result is a formula for multiplicity with which an irreducible representation ofK occurs in a generalized representation ofG arising not necessarily from fundamental Cartan subgroup ofG. This generalizes a result due to Enright and Wallach in a fundamental case. |
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Keywords: | Reductive Lie algebra and subgroup maximal compact group weight partition function multiplicity generalized principal series |
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