A Method for Weight Multiplicity Computation Based on Berezin Quantization
Let G be a compact semisimple Lie group and T be a maximal torus of G. We describe a method for weight multiplicity computation in unitary irreducible representations of G, based on the theory of Berezin quantization on G/T. Let Γhol(Lλ) be the reproducing kernel Hilbert space of holomorphic section...
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| Datum: | 2009 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2009
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/149125 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Method for Weight Multiplicity Computation Based on Berezin Quantization / D. Bar-Moshe // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let G be a compact semisimple Lie group and T be a maximal torus of G. We describe a method for weight multiplicity computation in unitary irreducible representations of G, based on the theory of Berezin quantization on G/T. Let Γhol(Lλ) be the reproducing kernel Hilbert space of holomorphic sections of the homogeneous line bundle Lλ over G/T associated with the highest weight λ of the irreducible representation πλ of G. The multiplicity of a weight m in πλ is computed from functional analytical structure of the Berezin symbol of the projector in Γhol(Lλ) onto subspace of weight m. We describe a method of the construction of this symbol and the evaluation of the weight multiplicity as a rank of a Hermitian form. The application of this method is described in a number of examples. |
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