Simple SL(n)-modules with normal closures of maximal torus orbits

Kuyumzhiyan, Karine

doi:10.1007/s10801-009-0175-2

Cited by 3 publications

(6 citation statements)

References 14 publications

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“…In the case G = SL(n) this particular problem was also solved earlier in [10,Example 3.7] and [11]. In the previous papers of the second author [6,7] all the simple G-modules having this property were found for all classical groups G. For the completeness, the results of [6,7] are included in the table in Theorem 1.…”

Section: Introductionmentioning

confidence: 69%

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Simple modules of exceptional groups with normal closures of maximal torus orbits

Bogdanov

Kuyumzhiyan

2012

Math Notes

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Let G be an exceptional simple algebraic group, and let T be a maximal torus in G. In this paper, for every such G, we find all simple rational G-modules V with the following property: for every vector v ∈ V , the closure of its T -orbit is a normal affine variety. For all G-modules without this property we present a T -orbit with the non-normal closure. To solve this problem, we use a combinatorial criterion of normality formulated in the terms of weights of a simple G-module. This paper continues [6] and [7], where the same problem was solved for classical linear groups.

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Section: Introductionmentioning

confidence: 69%

“…Root system Highest weight Checked in [6,8,10,11] A 1 3π 1 [6] Date: November 6, 2018. The first author is partially supported by the RFBR grant 20-01-00096, and by ADTP of the Ministry of Science and Education of Russian Federation, project 2.1.1/11133.…”

Section: Introductionmentioning

confidence: 99%

Simple modules of exceptional groups with normal closures of maximal torus orbits

Bogdanov

Kuyumzhiyan

2012

Math Notes

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“…Для группы = ( ) эта задача была также решена ранее в [2; пример 3.7] и [3]. В предыдущих работах второго автора [4], [5] найдены все простые модули всех классических групп, обладающие этим свойством. Для полноты картины результаты работ [4], [5] включены в таблицу в теореме 1.…”

Section: пустьunclassified

“…В предыдущих работах второго автора [4], [5] найдены все простые модули всех классических групп, обладающие этим свойством. Для полноты картины результаты работ [4], [5] включены в таблицу в теореме 1. Аналогичная задача для приводимых систем корней еще не исследована.…”

Section: пустьunclassified

Простые Модули Исключительных Групп С Нормальными Замыканиями Орбит Максимального Тора

Богданов¹,

Bogdanov²,

Куюмжиян³

et al. 2012

Mat. Zametki

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Работа первого автора выполнена при поддержке Российского фонда фундаментальных исследований (грант № 20-01-00096), а также АВЦП "Развитие научного потенциала высшей школы" Министерства образования и науки РФ (проект 2.1.1/11133). Работа второго автора выполнена при поддержке Лаборатории алгебраической геометрии НИУ ВШЭ, (грант правительства РФ, дог. 11.G34.31.0023), "EADS Foundation Chair in Mathematics", Российского фонда фундаментальных исследований (грант № 09-01-00648-a), Русско-французской лаборатории Понселе (UMI 2615 CNRS) и фонда "Династия".

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“…3.7] and [19]. In her previous paper [13] the author checks this property for all simple SL(n)modules. For exceptional root systems, this problem is studied in [1].…”

Section: Introductionmentioning

confidence: 99%

Simple modules of classical linear groups with normal closures of maximal torus orbits

Kuyumzhiyan

2012

Sib Math J

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Let T be a maximal torus in a classical linear group G. In this paper we find all simple rational G-modules V such that for each vector v ∈ V the closure of its T -orbit is a normal affine variety. For every other G-module we present a T -orbit with the non-normal closure. We use a combinatorial criterion of normality formulated in terms of the set of weights of a simple G-module. This work is a continuation of [13], where the same problem is solved in the case G = SL(n).

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Simple SL(n)-modules with normal closures of maximal torus orbits

Cited by 3 publications

References 14 publications

Simple modules of exceptional groups with normal closures of maximal torus orbits

Simple modules of exceptional groups with normal closures of maximal torus orbits

Простые Модули Исключительных Групп С Нормальными Замыканиями Орбит Максимального Тора

Simple modules of classical linear groups with normal closures of maximal torus orbits

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