The Primitive Derivation and Discrete Integrals
The modules of logarithmic derivations for the (extended) Catalan and Shi arrangements associated with root systems are known to be free. However, except for a few cases, explicit bases for such modules are not known. In this paper, we construct explicit bases for type root systems. Our constructio...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211311 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Primitive Derivation and Discrete Integrals. Daisuke Suyama and Masahiko Yoshinaga. SIGMA 17 (2021), 038, 9 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862739222659596288 |
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| author | Suyama, Daisuke Yoshinaga, Masahiko |
| author_facet | Suyama, Daisuke Yoshinaga, Masahiko |
| citation_txt | The Primitive Derivation and Discrete Integrals. Daisuke Suyama and Masahiko Yoshinaga. SIGMA 17 (2021), 038, 9 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The modules of logarithmic derivations for the (extended) Catalan and Shi arrangements associated with root systems are known to be free. However, except for a few cases, explicit bases for such modules are not known. In this paper, we construct explicit bases for type root systems. Our construction is based on Bandlow-Musiker's integral formula for a basis of the space of quasiinvariants. The integral formula can be considered as an expression for the inverse of the primitive derivation introduced by K. Saito. We prove that the discrete analogues of the integral formulas provide bases for Catalan and Shi arrangements.
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| first_indexed | 2026-04-17T17:22:34Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211311 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T17:22:34Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
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| spelling | Suyama, Daisuke Yoshinaga, Masahiko 2025-12-29T11:08:54Z 2021 The Primitive Derivation and Discrete Integrals. Daisuke Suyama and Masahiko Yoshinaga. SIGMA 17 (2021), 038, 9 pages 1815-0659 2020 Mathematics Subject Classification: 52C35; 20F55 arXiv:2009.13710 https://nasplib.isofts.kiev.ua/handle/123456789/211311 https://doi.org/10.3842/SIGMA.2021.038 The modules of logarithmic derivations for the (extended) Catalan and Shi arrangements associated with root systems are known to be free. However, except for a few cases, explicit bases for such modules are not known. In this paper, we construct explicit bases for type root systems. Our construction is based on Bandlow-Musiker's integral formula for a basis of the space of quasiinvariants. The integral formula can be considered as an expression for the inverse of the primitive derivation introduced by K. Saito. We prove that the discrete analogues of the integral formulas provide bases for Catalan and Shi arrangements. The authors thank Takuro Abe and Misha Feigin for many useful discussions on the topics. This work was partially supported by JSPS KAKENHI Grant Numbers JP18H01115 and JP15KK0144. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Primitive Derivation and Discrete Integrals Article published earlier |
| spellingShingle | The Primitive Derivation and Discrete Integrals Suyama, Daisuke Yoshinaga, Masahiko |
| title | The Primitive Derivation and Discrete Integrals |
| title_full | The Primitive Derivation and Discrete Integrals |
| title_fullStr | The Primitive Derivation and Discrete Integrals |
| title_full_unstemmed | The Primitive Derivation and Discrete Integrals |
| title_short | The Primitive Derivation and Discrete Integrals |
| title_sort | primitive derivation and discrete integrals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211311 |
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