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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149125 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862590334951751680 |
|---|---|
| author | Bar-Moshe, D. |
| author_facet | Bar-Moshe, D. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-27T04:31:34Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149125 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T04:31:34Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bar-Moshe, D. 2019-02-19T17:33:12Z 2019-02-19T17:33:12Z 2009 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 https://nasplib.isofts.kiev.ua/handle/123456789/149125 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. I would like to express my sincere gratitude to R. Pnini for his kind help and support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Method for Weight Multiplicity Computation Based on Berezin Quantization Article published earlier |
| spellingShingle | A Method for Weight Multiplicity Computation Based on Berezin Quantization Bar-Moshe, D. |
| title | 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_short | A Method for Weight Multiplicity Computation Based on Berezin Quantization |
| title_sort | method for weight multiplicity computation based on berezin quantization |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149125 |
| work_keys_str_mv | AT barmoshed amethodforweightmultiplicitycomputationbasedonberezinquantization AT barmoshed methodforweightmultiplicitycomputationbasedonberezinquantization |