Polynomiality of factorizations in reflection groups. (9th February 2023) - Polak, Elzbieta; Ross, Dustin
Abstract: We study the number of ways of factoring elements in the complex reflection groups $G(r, s, n)$ as products of reflections. We prove a result that compares factorization numbers in $G(r, s, n)$ to those in the symmetric group $S_n$, and we use this comparison, along with the Ekedahl, Lando, Shapiro, and Vainshtein (ELSV) formula, to deduce a polynomial structure for factorizations in $G(r, s, n)$ .