Consecutive patterns, Kostant's problem and type A6.
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| Title: | Consecutive patterns, Kostant's problem and type A6. |
|---|---|
| Authors: | Creedon, Samuel1 (AUTHOR) samuel.creedon@math.uu.se, Mazorchuk, Volodymyr1 (AUTHOR) mazor@math.uu.se |
| Source: | International Journal of Algebra & Computation. Jun2026, Vol. 36 Issue 4, p317-356. 40p. |
| Subjects: | Lie algebras, Patterns (Mathematics), Mathematical category theory, Modules (Algebra), Symmetry groups, Indecomposable modules |
| Abstract: | For a permutation w in the symmetric group n , let L (w) denote the simple highest weight module in the principal block of the BGG category for the Lie algebra n (ℂ). We first prove that L (w) is Kostant negative whenever w consecutively contains certain patterns. We then provide a complete answer to Kostant's problem in type A 6 and show that the indecomposability conjecture also holds in type A 6 , that is, applying an indecomposable projective functor to a simple module outputs either an indecomposable module or zero. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company 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: 193893247 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Consecutive patterns, Kostant's problem and type A6. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Creedon%2C+Samuel%22">Creedon, Samuel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> samuel.creedon@math.uu.se</i><br /><searchLink fieldCode="AR" term="%22Mazorchuk%2C+Volodymyr%22">Mazorchuk, Volodymyr</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mazor@math.uu.se</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Algebra+%26+Computation%22">International Journal of Algebra & Computation</searchLink>. Jun2026, Vol. 36 Issue 4, p317-356. 40p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Lie+algebras%22">Lie algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Patterns+%28Mathematics%29%22">Patterns (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+category+theory%22">Mathematical category theory</searchLink><br /><searchLink fieldCode="DE" term="%22Modules+%28Algebra%29%22">Modules (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+groups%22">Symmetry groups</searchLink><br /><searchLink fieldCode="DE" term="%22Indecomposable+modules%22">Indecomposable modules</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: For a permutation w in the symmetric group n , let L (w) denote the simple highest weight module in the principal block of the BGG category for the Lie algebra n (ℂ). We first prove that L (w) is Kostant negative whenever w consecutively contains certain patterns. We then provide a complete answer to Kostant's problem in type A 6 and show that the indecomposability conjecture also holds in type A 6 , that is, applying an indecomposable projective functor to a simple module outputs either an indecomposable module or zero. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company 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: 10.1142/S0218196726500116 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 40 StartPage: 317 Subjects: – SubjectFull: Lie algebras Type: general – SubjectFull: Patterns (Mathematics) Type: general – SubjectFull: Mathematical category theory Type: general – SubjectFull: Modules (Algebra) Type: general – SubjectFull: Symmetry groups Type: general – SubjectFull: Indecomposable modules Type: general Titles: – TitleFull: Consecutive patterns, Kostant's problem and type A6. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Creedon, Samuel – PersonEntity: Name: NameFull: Mazorchuk, Volodymyr IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02181967 Numbering: – Type: volume Value: 36 – Type: issue Value: 4 Titles: – TitleFull: International Journal of Algebra & Computation Type: main |
| ResultId | 1 |
