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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | 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 |
| Zitieren: | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3. Frank Wang and Eric Yee. SIGMA 21 (2025), 057, 24 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862666365203120128 |
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| author | Wang, Frank Yee, Eric |
| author_facet | Wang, Frank Yee, Eric |
| citation_txt | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3. Frank Wang and Eric Yee. SIGMA 21 (2025), 057, 24 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-16T09:29:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213519 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T09:29:07Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Wang, Frank Yee, Eric 2026-02-18T11:23:25Z 2025 Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3. Frank Wang and Eric Yee. SIGMA 21 (2025), 057, 24 pages 1815-0659 2020 Mathematics Subject Classification: 81R12; 13A50; 20C08 arXiv:2412.20673 https://nasplib.isofts.kiev.ua/handle/123456789/213519 https://doi.org/10.3842/SIGMA.2025.057 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. We would like to thank the PRIMES program for making the project possible. We would also like to thank the referees for their useful comments and suggestions. This material is based upon work supported under the National Science Foundation Graduate Research Fellowship under Grant No. 2141064. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3 Article published earlier |
| spellingShingle | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3 Wang, Frank Yee, Eric |
| title | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3 |
| title_full | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3 |
| title_fullStr | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3 |
| title_full_unstemmed | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3 |
| title_short | Hilbert Series of ₃-Quasi-Invariant Polynomials in Characteristics 2, 3 |
| title_sort | hilbert series of ₃-quasi-invariant polynomials in characteristics 2, 3 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213519 |
| work_keys_str_mv | AT wangfrank hilbertseriesof3quasiinvariantpolynomialsincharacteristics23 AT yeeeric hilbertseriesof3quasiinvariantpolynomialsincharacteristics23 |