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The Primitive Derivation and Discrete Integrals

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Title: The Primitive Derivation and Discrete Integrals
Authors: Suyama, Daisuke Browse this author
Yoshinaga, Masahiko Browse this author →KAKEN DB
Keywords: hyperplane arrangements
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
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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