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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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491252019-02-20T01:25:25Z A Method for Weight Multiplicity Computation Based on Berezin Quantization Bar-Moshe, D. 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. 2009 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bar-Moshe, D. |
| spellingShingle |
Bar-Moshe, D. A Method for Weight Multiplicity Computation Based on Berezin Quantization Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bar-Moshe, D. |
| author_sort |
Bar-Moshe, D. |
| title |
A Method for Weight Multiplicity Computation Based on Berezin Quantization |
| title_short |
A Method for Weight Multiplicity Computation Based on Berezin Quantization |
| title_full |
A Method for Weight Multiplicity Computation Based on Berezin Quantization |
| title_fullStr |
A Method for Weight Multiplicity Computation Based on Berezin Quantization |
| title_full_unstemmed |
A Method for Weight Multiplicity Computation Based on Berezin Quantization |
| title_sort |
method for weight multiplicity computation based on berezin quantization |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149125 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:32:10Z |
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