Degree-One Rational Cherednik Algebras for the Symmetric Group
Drinfeld orbifold algebras deform skew group algebras in polynomial degree at most one and hence encompass graded Hecke algebras, and in particular symplectic reflection algebras and rational Cherednik algebras. We introduce parametrized families of Drinfeld orbifold algebras for symmetric groups ac...
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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/123456789/211310 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Degree-One Rational Cherednik Algebras for the Symmetric Group. Briana Foster-Greenwood and Cathy Kriloff. SIGMA 17 (2021), 039, 35 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862558522113261568 |
|---|---|
| author | Foster-Greenwood, Briana Kriloff, Cathy |
| author_facet | Foster-Greenwood, Briana Kriloff, Cathy |
| citation_txt | Degree-One Rational Cherednik Algebras for the Symmetric Group. Briana Foster-Greenwood and Cathy Kriloff. SIGMA 17 (2021), 039, 35 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Drinfeld orbifold algebras deform skew group algebras in polynomial degree at most one and hence encompass graded Hecke algebras, and in particular symplectic reflection algebras and rational Cherednik algebras. We introduce parametrized families of Drinfeld orbifold algebras for symmetric groups acting on doubled representations that generalize rational Cherednik algebras by deforming in degree one. We characterize rich families of maps recording commutator relations with their linear parts supported only on and only off the identity when the symmetric group acts on the natural permutation representation plus its dual. This produces degree-one versions of ₙ-type rational Cherednik algebras. When the symmetric group acts on the standard irreducible reflection representation plus its dual, there are no degree-one Lie orbifold algebra maps, but there is a three-parameter family of Drinfeld orbifold algebras arising from maps supported only off the identity. These provide degree-one generalizations of the ₙ-type rational Cherednik algebras ₀ ̦c.
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| first_indexed | 2026-03-13T07:33:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211310 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T07:33:23Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Foster-Greenwood, Briana Kriloff, Cathy 2025-12-29T11:08:22Z 2021 Degree-One Rational Cherednik Algebras for the Symmetric Group. Briana Foster-Greenwood and Cathy Kriloff. SIGMA 17 (2021), 039, 35 pages 1815-0659 2020 Mathematics Subject Classification: 16S80; 16E40; 16S35; 20B30 arXiv:1912.06743 https://nasplib.isofts.kiev.ua/handle/123456789/211310 https://doi.org/10.3842/SIGMA.2021.039 Drinfeld orbifold algebras deform skew group algebras in polynomial degree at most one and hence encompass graded Hecke algebras, and in particular symplectic reflection algebras and rational Cherednik algebras. We introduce parametrized families of Drinfeld orbifold algebras for symmetric groups acting on doubled representations that generalize rational Cherednik algebras by deforming in degree one. We characterize rich families of maps recording commutator relations with their linear parts supported only on and only off the identity when the symmetric group acts on the natural permutation representation plus its dual. This produces degree-one versions of ₙ-type rational Cherednik algebras. When the symmetric group acts on the standard irreducible reflection representation plus its dual, there are no degree-one Lie orbifold algebra maps, but there is a three-parameter family of Drinfeld orbifold algebras arising from maps supported only off the identity. These provide degree-one generalizations of the ₙ-type rational Cherednik algebras ₀ ̦c. We thank the referees for helpful suggestions and questions that improved the writing of the paper, particularly those that prompted us to add Proposition6.1, improve Section 4.5, and reorganize overall. We also thank Lily Silverstein for helpful conversations related to Section 4.5. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Degree-One Rational Cherednik Algebras for the Symmetric Group Article published earlier |
| spellingShingle | Degree-One Rational Cherednik Algebras for the Symmetric Group Foster-Greenwood, Briana Kriloff, Cathy |
| title | Degree-One Rational Cherednik Algebras for the Symmetric Group |
| title_full | Degree-One Rational Cherednik Algebras for the Symmetric Group |
| title_fullStr | Degree-One Rational Cherednik Algebras for the Symmetric Group |
| title_full_unstemmed | Degree-One Rational Cherednik Algebras for the Symmetric Group |
| title_short | Degree-One Rational Cherednik Algebras for the Symmetric Group |
| title_sort | degree-one rational cherednik algebras for the symmetric group |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211310 |
| work_keys_str_mv | AT fostergreenwoodbriana degreeonerationalcherednikalgebrasforthesymmetricgroup AT kriloffcathy degreeonerationalcherednikalgebrasforthesymmetricgroup |