A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups.

Autor: Takuro Abe, Röhrle, Gerhard, Stump, Christian, Masahiko Yoshinaga
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Zdroj: Journal of Combinatorial Algebra; 2024, Vol. 8 Issue 3/4, p251-278, 28p
Abstrakt: Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration of that module. Our approach is based on a detailed analysis of a flat connection applied to the primitive vector field. This generalizes and unifies analogous results for real reflection groups. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index