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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2025 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213519 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
|
|---|---|
| ISSN: | 1815-0659 |