Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3
We compute the Hilbert series of the space of = 3 variable quasi-invariant polynomials in characteristic 2 and 3, capturing the dimension of the homogeneous components of the space, and explicitly describe the generators in the characteristic 2 case. In doing so, we extend the work of the first aut...
Збережено в:
| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| ISSN: | 1815-0659 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/213519 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3. Frank Wang and Eric Yee. SIGMA 21 (2025), 057, 24 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We compute the Hilbert series of the space of = 3 variable quasi-invariant polynomials in characteristic 2 and 3, capturing the dimension of the homogeneous components of the space, and explicitly describe the generators in the characteristic 2 case. In doing so, we extend the work of the first author in 2023 on quasi-invariant polynomials in characteristic > and prove that a sufficient condition found by Ren-Xu in 2020 on when the Hilbert series differs between characteristic 0 and is also necessary for = 3, = 2,3. This is the first description of quasi-invariant polynomials in the case where the space forms a modular representation over the symmetric group, bringing us closer to describing the quasi-invariant polynomials in all characteristics and numbers of variables.
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| ISSN: | 1815-0659 |