Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1.
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| Title: | Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1. |
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| Authors: | Nazarov, Anton1 (AUTHOR) antonnaz@gmail.com, Nikitin, Pavel2,3 (AUTHOR), Postnova, Olga4 (AUTHOR) |
| Source: | Journal of Physics A: Mathematical & Theoretical. 3/31/2023, Vol. 56 Issue 13, p1-33. 33p. |
| Subjects: | Lie algebras, Central limit theorem, Probability measures, Tensor products, Algebra |
| Abstract: | We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of s o 2 n + 1 . The irreducible representations correspond to the generalized Young diagrams. With respect to this measure the probability of an irreducible representation is the product of its multiplicity and dimension, divided by the total dimension of the tensor product. We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N / n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 162473542 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Nazarov%2C+Anton%22">Nazarov, Anton</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> antonnaz@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Nikitin%2C+Pavel%22">Nikitin, Pavel</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Postnova%2C+Olga%22">Postnova, Olga</searchLink><relatesTo>4</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 3/31/2023, Vol. 56 Issue 13, p1-33. 33p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Lie+algebras%22">Lie algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Central+limit+theorem%22">Central limit theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+measures%22">Probability measures</searchLink><br /><searchLink fieldCode="DE" term="%22Tensor+products%22">Tensor products</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of s o 2 n + 1 . The irreducible representations correspond to the generalized Young diagrams. With respect to this measure the probability of an irreducible representation is the product of its multiplicity and dimension, divided by the total dimension of the tensor product. We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N / n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/1751-8121/acbd73 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 33 StartPage: 1 Subjects: – SubjectFull: Lie algebras Type: general – SubjectFull: Central limit theorem Type: general – SubjectFull: Probability measures Type: general – SubjectFull: Tensor products Type: general – SubjectFull: Algebra Type: general Titles: – TitleFull: Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Nazarov, Anton – PersonEntity: Name: NameFull: Nikitin, Pavel – PersonEntity: Name: NameFull: Postnova, Olga IsPartOfRelationships: – BibEntity: Dates: – D: 31 M: 03 Text: 3/31/2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 17518113 Numbering: – Type: volume Value: 56 – Type: issue Value: 13 Titles: – TitleFull: Journal of Physics A: Mathematical & Theoretical Type: main |
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