Singularities of Schubert Varieties within a Right Cell
We describe an algorithm that pattern embeds, in the sense of Woo-Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan-Lusztig cell. This apparently harmless fact has applications in finding examples of reducible associated varieties of ₙ-highe...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211353 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Singularities of Schubert Varieties within a Right Cell. Martina Lanini and Peter J. McNamara. SIGMA 17 (2021), 070, 9 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862650035332710400 |
|---|---|
| author | Lanini, Martina McNamara, Peter J. |
| author_facet | Lanini, Martina McNamara, Peter J. |
| citation_txt | Singularities of Schubert Varieties within a Right Cell. Martina Lanini and Peter J. McNamara. SIGMA 17 (2021), 070, 9 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We describe an algorithm that pattern embeds, in the sense of Woo-Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan-Lusztig cell. This apparently harmless fact has applications in finding examples of reducible associated varieties of ₙ-highest weight modules, as well as in the study of W-graphs for symmetric groups, and in comparing various bases of irreducible representations of the symmetric group or its Hecke algebra. For example, we can systematically produce many negative answers to a question from the 1980s of Borho-Brylinski and Joseph, which had been settled by Williamson via computer calculations only in 2014.
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| first_indexed | 2026-03-15T14:41:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211353 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T14:41:17Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lanini, Martina McNamara, Peter J. 2025-12-30T15:54:15Z 2021 Singularities of Schubert Varieties within a Right Cell. Martina Lanini and Peter J. McNamara. SIGMA 17 (2021), 070, 9 pages 1815-0659 2020 Mathematics Subject Classification: 14M15; 20B30; 32C38; 20C08 arXiv:2003.08616 https://nasplib.isofts.kiev.ua/handle/123456789/211353 https://doi.org/10.3842/SIGMA.2021.070 We describe an algorithm that pattern embeds, in the sense of Woo-Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan-Lusztig cell. This apparently harmless fact has applications in finding examples of reducible associated varieties of ₙ-highest weight modules, as well as in the study of W-graphs for symmetric groups, and in comparing various bases of irreducible representations of the symmetric group or its Hecke algebra. For example, we can systematically produce many negative answers to a question from the 1980s of Borho-Brylinski and Joseph, which had been settled by Williamson via computer calculations only in 2014. The authors would like to thank the Institut Henri Poincaré in Paris and the organisers of the Representation Theory Trimester. M.L. acknowledges the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006, and the PRIN2017 CUP E8419000480006. P.M. acknowledges support from ARC grants DE150101415 and DP180103150. We thank G. Williamson for useful conversations and the anonymous referees for their valuable input. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Singularities of Schubert Varieties within a Right Cell Article published earlier |
| spellingShingle | Singularities of Schubert Varieties within a Right Cell Lanini, Martina McNamara, Peter J. |
| title | Singularities of Schubert Varieties within a Right Cell |
| title_full | Singularities of Schubert Varieties within a Right Cell |
| title_fullStr | Singularities of Schubert Varieties within a Right Cell |
| title_full_unstemmed | Singularities of Schubert Varieties within a Right Cell |
| title_short | Singularities of Schubert Varieties within a Right Cell |
| title_sort | singularities of schubert varieties within a right cell |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211353 |
| work_keys_str_mv | AT laninimartina singularitiesofschubertvarietieswithinarightcell AT mcnamarapeterj singularitiesofschubertvarietieswithinarightcell |