Projective representations and spin characters of complex reflection groups G(m,p,n) and G(m,p,∞), III

Abstract

Based on the hereditary property from “mother groups” $G(m,1,n)$, $4\le n\le \mathrm{\infty }$, to their “child groups” $G(m,p,n)$, $p|m,p>1$, the so-called complex reflection groups studied in previous work with E. Hirai, we provide a detailed study of the classification and construction first of irreducible projective representations (i.e., spin representations) and their characters of the generalized symmetric groups $G(m,1,n)$, and then of spin characters of the inductive limit groups $G(m,1,\mathrm{\infty })$. By further studying the heredity, we give the main kernel of the results for the child groups with $p|m,p>1$.