Integral expressions for derivations of multiarrangements
Misha Feigin, Zixuan Wang, Masahiko Yoshinaga
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Source: Crossref
Published: Dec 20, 2024
DOI: 10.1142/s0129167x2450085x
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The construction of an explicit basis for a free multiarrangement is not easy in general. Inspired by the integral expressions for quasi-invariants of the symmetric group, we present integral expressions for specific bases of certain multiarrangements. Our construction covers the cases of three lines in dimension [Formula: see text] (previously examined by Wakamiko) and free multiarrangements associated with complex reflection groups (Hoge, Mano, Röhrle, Stump). Furthermore, we propose a conjectural basis for the module of logarithmic vector fields of the extended Catalan arrangement of type [Formula: see text].
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