Quasi-Invariants in Characteristic and Twisted Quasi-Invariants
The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 was computed by Feigin and Veselov [Int. Math. Res. Not. 2002 (2002), 521-545]. In this paper, we show some partial results a...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211013 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants. Michael Ren and Xiaomeng Xu. SIGMA 16 (2020), 107, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862632767208030208 |
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| author | Ren, Michael Xu, Xiaomeng |
| author_facet | Ren, Michael Xu, Xiaomeng |
| citation_txt | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants. Michael Ren and Xiaomeng Xu. SIGMA 16 (2020), 107, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 was computed by Feigin and Veselov [Int. Math. Res. Not. 2002 (2002), 521-545]. In this paper, we show some partial results and make two conjectures on the Hilbert series of these spaces over fields of positive characteristic. On the other hand, Braverman, Etingof, and Finkelberg [arXiv:1611.10216] introduced the spaces of quasi-invariant polynomials twisted by a monomial. We extend some of their results to the spaces twisted by a smooth function.
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| first_indexed | 2026-03-14T20:34:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211013 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T20:34:05Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
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| spelling | Ren, Michael Xu, Xiaomeng 2025-12-22T09:28:21Z 2020 Quasi-Invariants in Characteristic and Twisted Quasi-Invariants. Michael Ren and Xiaomeng Xu. SIGMA 16 (2020), 107, 13 pages 1815-0659 2020 Mathematics Subject Classification: 81R12; 20C08 arXiv:1907.13417 https://nasplib.isofts.kiev.ua/handle/123456789/211013 https://doi.org/10.3842/SIGMA.2020.107 The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 was computed by Feigin and Veselov [Int. Math. Res. Not. 2002 (2002), 521-545]. In this paper, we show some partial results and make two conjectures on the Hilbert series of these spaces over fields of positive characteristic. On the other hand, Braverman, Etingof, and Finkelberg [arXiv:1611.10216] introduced the spaces of quasi-invariant polynomials twisted by a monomial. We extend some of their results to the spaces twisted by a smooth function. We would like to thank MIT PRIMES, specifically Pavel Etingof, for suggesting the project. We would like to thank Eric Rains for the very useful discussions. We also would like to thank the referees for carefully reading our manuscript and for their valuable comments and suggestions, which substantially helped to improve the readability and quality of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quasi-Invariants in Characteristic and Twisted Quasi-Invariants Article published earlier |
| spellingShingle | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants Ren, Michael Xu, Xiaomeng |
| title | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants |
| title_full | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants |
| title_fullStr | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants |
| title_full_unstemmed | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants |
| title_short | Quasi-Invariants in Characteristic and Twisted Quasi-Invariants |
| title_sort | quasi-invariants in characteristic and twisted quasi-invariants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211013 |
| work_keys_str_mv | AT renmichael quasiinvariantsincharacteristicandtwistedquasiinvariants AT xuxiaomeng quasiinvariantsincharacteristicandtwistedquasiinvariants |