A Method for Weight Multiplicity Computation Based on Berezin Quantization
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Method for Weight Multiplicity Computation Based on Berezin Quantization
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| Creator |
Bar-Moshe, D.
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| Description |
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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| Date |
2019-02-19T17:33:12Z
2019-02-19T17:33:12Z 2009 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2000 Mathematics Subject Classification: 22E46; 32M05; 32M10; 53D50; 81Q70 http://dspace.nbuv.gov.ua/handle/123456789/149125 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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