Non-commutative creation operators for symmetric polynomials.
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| Title: | Non-commutative creation operators for symmetric polynomials. |
|---|---|
| Authors: | Mironov, A.1,2,3 (AUTHOR) mironov@lpi.ru, Morozov, A.2,3,4 (AUTHOR) morozov@itep.ru |
| Source: | European Physical Journal C -- Particles & Fields. May2026, Vol. 86 Issue 5, p1-13. 13p. |
| Subjects: | Symmetric functions, Operator functions, Partitions (Mathematics), Algebra, Schur functions |
| Abstract: | We reconsider in modern terms the old discovery by A. Kirillov and M. Noumi, who devised peculiar operators adding columns to Young diagrams enumerating the Schur, Jack and Macdonald polynomials. In this sense, these are a kind of "creation" operators, representing Pieri rules in a maximally simple form, when boxes are added to Young diagrams in a regular way and not to arbitrary "empty places" around the diagram. Instead the operators do not commute, and one should add columns of different lengths one after another. We consider this construction in different contexts. In particular, we build up the creation operators B ^ m in the matrix and Fock representations of the W 1 + ∞ algebra, and in the Fock representation of the affine Yangian algebra Y ( gl ^ 1) . [ABSTRACT FROM AUTHOR] |
| Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194633847 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Non-commutative creation operators for symmetric polynomials. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mironov%2C+A%2E%22">Mironov, A.</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> mironov@lpi.ru</i><br /><searchLink fieldCode="AR" term="%22Morozov%2C+A%2E%22">Morozov, A.</searchLink><relatesTo>2,3,4</relatesTo> (AUTHOR)<i> morozov@itep.ru</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. May2026, Vol. 86 Issue 5, p1-13. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Symmetric+functions%22">Symmetric functions</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+functions%22">Operator functions</searchLink><br /><searchLink fieldCode="DE" term="%22Partitions+%28Mathematics%29%22">Partitions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Schur+functions%22">Schur functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We reconsider in modern terms the old discovery by A. Kirillov and M. Noumi, who devised peculiar operators adding columns to Young diagrams enumerating the Schur, Jack and Macdonald polynomials. In this sense, these are a kind of "creation" operators, representing Pieri rules in a maximally simple form, when boxes are added to Young diagrams in a regular way and not to arbitrary "empty places" around the diagram. Instead the operators do not commute, and one should add columns of different lengths one after another. We consider this construction in different contexts. In particular, we build up the creation operators B ^ m in the matrix and Fock representations of the W 1 + ∞ algebra, and in the Fock representation of the affine Yangian algebra Y ( gl ^ 1) . [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature 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: 10.1140/epjc/s10052-026-15634-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 1 Subjects: – SubjectFull: Symmetric functions Type: general – SubjectFull: Operator functions Type: general – SubjectFull: Partitions (Mathematics) Type: general – SubjectFull: Algebra Type: general – SubjectFull: Schur functions Type: general Titles: – TitleFull: Non-commutative creation operators for symmetric polynomials. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mironov, A. – PersonEntity: Name: NameFull: Morozov, A. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 14346044 Numbering: – Type: volume Value: 86 – Type: issue Value: 5 Titles: – TitleFull: European Physical Journal C -- Particles & Fields Type: main |
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