Modules with Demazure Flags and Character Formulae
In this paper we study a family of finite-dimensional graded representations of the current algebra of sl₂ which are indexed by partitions. We show that these representations admit a flag where the successive quotients are Demazure modules which occur in a level ℓ-integrable module for A₁¹ as long a...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146820 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modules with Demazure Flags and Character Formulae / V. Chari, L. Schneider, P. Shereen, J. Wand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 16 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862614801890410496 |
|---|---|
| author | Chari, V. Schneider, L. Shereen, P. Wand, J. |
| author_facet | Chari, V. Schneider, L. Shereen, P. Wand, J. |
| citation_txt | Modules with Demazure Flags and Character Formulae / V. Chari, L. Schneider, P. Shereen, J. Wand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper we study a family of finite-dimensional graded representations of the current algebra of sl₂ which are indexed by partitions. We show that these representations admit a flag where the successive quotients are Demazure modules which occur in a level ℓ-integrable module for A₁¹ as long as ℓ is large. We associate to each partition and to each ℓ an edge-labeled directed graph which allows us to describe in a combinatorial way the graded multiplicity of a given level ℓ-Demazure module in the filtration. In the special case of the partition 1s and ℓ=2, we give a closed formula for the graded multiplicity of level two Demazure modules in a level one Demazure module. As an application, we use our result along with the results of Naoi and Lenart et al., to give the character of a g-stable level one Demazure module associated to B¹n as an explicit combination of suitably specialized Macdonald polynomials. In the case of sl₂, we also study the filtration of the level two Demazure module by level three Demazure modules and compute the numerical filtration multiplicities and show that the graded multiplicites are related to (variants of) partial theta series.
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| first_indexed | 2025-11-29T10:46:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146820 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-29T10:46:14Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chari, V. Schneider, L. Shereen, P. Wand, J. 2019-02-11T16:22:41Z 2019-02-11T16:22:41Z 2014 Modules with Demazure Flags and Character Formulae / V. Chari, L. Schneider, P. Shereen, J. Wand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 06B15 ; 05E10; 14H42 DOI:10.3842/SIGMA.2014.032 https://nasplib.isofts.kiev.ua/handle/123456789/146820 In this paper we study a family of finite-dimensional graded representations of the current algebra of sl₂ which are indexed by partitions. We show that these representations admit a flag where the successive quotients are Demazure modules which occur in a level ℓ-integrable module for A₁¹ as long as ℓ is large. We associate to each partition and to each ℓ an edge-labeled directed graph which allows us to describe in a combinatorial way the graded multiplicity of a given level ℓ-Demazure module in the filtration. In the special case of the partition 1s and ℓ=2, we give a closed formula for the graded multiplicity of level two Demazure modules in a level one Demazure module. As an application, we use our result along with the results of Naoi and Lenart et al., to give the character of a g-stable level one Demazure module associated to B¹n as an explicit combination of suitably specialized Macdonald polynomials. In the case of sl₂, we also study the filtration of the level two Demazure module by level three Demazure modules and compute the numerical filtration multiplicities and show that the graded multiplicites are related to (variants of) partial theta series. This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full
 collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html.
 The authors thank S. Viswanath for discussions regarding the graph H`(ξ) and for drawing their
 attention to the connection of the results of Subsection 3.10 to partial theta series. The first and
 third authors acknowledge the hospitality and excellent working conditions at the Institute of
 Mathematical Sciences, Chennai, India where part of this work was done. They also thank the
 referees of the paper for their careful reading of the paper and for their many valuable comments.
 The first author was partially supported by DMS-0901253 and DMS-1303052. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Modules with Demazure Flags and Character Formulae Article published earlier |
| spellingShingle | Modules with Demazure Flags and Character Formulae Chari, V. Schneider, L. Shereen, P. Wand, J. |
| title | Modules with Demazure Flags and Character Formulae |
| title_full | Modules with Demazure Flags and Character Formulae |
| title_fullStr | Modules with Demazure Flags and Character Formulae |
| title_full_unstemmed | Modules with Demazure Flags and Character Formulae |
| title_short | Modules with Demazure Flags and Character Formulae |
| title_sort | modules with demazure flags and character formulae |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146820 |
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