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arXiv · 2309.01287

Integral expressions for derivations of multiarrangements

Misha Feigin·Zixuan Wang·Masahiko Yoshinaga
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Abstract

The construction of an explicit basis for a free multiarrangement is not easy in general. Inspired by the integral expressions for quasi-invariants of quantum Calogero-Moser systems, we present integral expressions for specific bases of certain multiarrangements. Our construction covers the cases of three lines in dimension $2$ (previously examined by Wakamiko) and free multiarrangements associated with complex reflection groups (Hoge, Mano, R\"ohrle, Stump). Furthermore, we propose a conjectural basis for the module of logarithmic vector fields of the extended Catalan arrangement of type $B_2$.

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Misha Feigin, Zixuan Wang, Masahiko Yoshinaga. 2023-09-03. Integral expressions for derivations of multiarrangements. https://arxiv.org/abs/2309.01287

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