Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
| Autor: | Douvropoulos, Theo, Lewis, Joel Brewster, Morales, Alejandro H. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Algebra, vol. 641 (2024), pp. 648-715 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2023.11.015 |
| Popis: | We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections $\operatorname{Red}_W(g)$ of reduced reflection factorizations of $g$ and $\operatorname{RGS}(W,g)$ of the relative generating sets of $g$. We compute the cardinalities of these sets for large families of parabolic quasi-Coxeter elements and, in particular, we relate the size $\#\operatorname{Red}_W(g)$ with geometric invariants of Frobenius manifolds. This paper is second in a series of three; we will rely on many of its results in part III to prove uniform formulas that enumerate full reflection factorizations of parabolic quasi-Coxeter elements, generalizing the genus-$0$ Hurwitz numbers. Comment: v2: 50 pages, minor edits, comments very much welcome! |
| Databáze: | arXiv |
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