Polynomiality of factorizations in reflection groups. (9th February 2023)

• Record Type: Journal Article
• Authors: Polak, Elzbieta; Ross, Dustin
• Is Part Of: Canadian journal of mathematics. Volume 75:Number 1(2023)
• Page Start: 245
• Page End: 266
• Publication Date: 2023-02-09
• Subjects: 20F55 -- 05A15; Reflection groups -- factorizations -- ELSV formula -- polynomiality; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/S0008414X21000663
• Languages: English
• ISSNs: 0008-414X

Abstract

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 $G(r, s, n)$ .