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The Primitive Derivation and Discrete Integrals
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: hyperplane arrangements, freeness, Shi arrangements.
Mots-clés : Catalan arrangements 
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     author = {Daisuke Suyama and Masahiko Yoshinaga},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a37/}
}
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Daisuke Suyama; Masahiko Yoshinaga. The Primitive Derivation and Discrete Integrals. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a37/

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