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The Primitive Derivation and Discrete Integrals
| Title: | The Primitive Derivation and Discrete Integrals |
| Authors: | Suyama, Daisuke Browse this author | | Yoshinaga, Masahiko Browse this author →KAKEN DB |
| Keywords: | hyperplane arrangements | | freeness | | Catalan arrangements | | Shi arrangements |
| Issue Date: | 23-Jun-2021 |
| Publisher: | Institute of Mathematics of the National Academy of Sciences of Ukraine |
| Journal Title: | Symmetry integrability and geometry-methods and applications |
| Volume: | 17 |
| Start Page: | 038 |
| Publisher DOI: | 10.3842/SIGMA.2021.038 |
| Abstract: | 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 A 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. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/81982 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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