On simple modules with singular highest weights for so2l+1(K)
In this paper, we study formal characters of simple modules with singular highest weights over classical Lie algebras of type B over an algebraically closed field of characteristic p ≥ h, where h is the Coxeter number. Assume that the highest weights of these simple modules are restricted. We have...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/466 |
| _version_ | 1797372653467598848 |
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| author | Sh.Sh. Ibraev A.Zh. Seitmuratov L.S. Kainbayeva |
| author_facet | Sh.Sh. Ibraev A.Zh. Seitmuratov L.S. Kainbayeva |
| author_sort | Sh.Sh. Ibraev |
| collection | DOAJ |
| description |
In this paper, we study formal characters of simple modules with singular highest weights over classical Lie algebras of type B over an algebraically closed field of characteristic p ≥ h, where h is the Coxeter number. Assume that the highest weights of these simple modules are restricted. We have given a description of their formal characters. In particular, we have obtained some new examples of simple Weyl modules. In the restricted region, the representation theory of algebraic groups and its Lie algebras are equivalent. Therefore, we can use the tools of the representation theory of semisimple and simply-connected algebraic groups in positive characteristic. To describe the formal characters of simple modules, we construct Jantzen filtrations of Weyl modules of the corresponding highest weights.
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| first_indexed | 2024-03-08T18:38:58Z |
| format | Article |
| id | doaj.art-5e8baf55ceac4d85b0a383301571df0d |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:58Z |
| publishDate | 2022-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-5e8baf55ceac4d85b0a383301571df0d2023-12-29T10:19:33ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-03-01105110.31489/2022m1/52-65On simple modules with singular highest weights for so2l+1(K)Sh.Sh. IbraevA.Zh. SeitmuratovL.S. Kainbayeva In this paper, we study formal characters of simple modules with singular highest weights over classical Lie algebras of type B over an algebraically closed field of characteristic p ≥ h, where h is the Coxeter number. Assume that the highest weights of these simple modules are restricted. We have given a description of their formal characters. In particular, we have obtained some new examples of simple Weyl modules. In the restricted region, the representation theory of algebraic groups and its Lie algebras are equivalent. Therefore, we can use the tools of the representation theory of semisimple and simply-connected algebraic groups in positive characteristic. To describe the formal characters of simple modules, we construct Jantzen filtrations of Weyl modules of the corresponding highest weights. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/466Lie algebrasimple modulealgebraic groupWeyl moduleJantzen filtration |
| spellingShingle | Sh.Sh. Ibraev A.Zh. Seitmuratov L.S. Kainbayeva On simple modules with singular highest weights for so2l+1(K) Қарағанды университетінің хабаршысы. Математика сериясы Lie algebra simple module algebraic group Weyl module Jantzen filtration |
| title | On simple modules with singular highest weights for so2l+1(K) |
| title_full | On simple modules with singular highest weights for so2l+1(K) |
| title_fullStr | On simple modules with singular highest weights for so2l+1(K) |
| title_full_unstemmed | On simple modules with singular highest weights for so2l+1(K) |
| title_short | On simple modules with singular highest weights for so2l+1(K) |
| title_sort | on simple modules with singular highest weights for so2l 1 k |
| topic | Lie algebra simple module algebraic group Weyl module Jantzen filtration |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/466 |
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