Kyoto J. Math. 62 (1), 1-94, (April 2022) DOI: 10.1215/21562261-2021-0019
Takeshi Hirai, Akihito Hora
KEYWORDS: projective representations and characters, spin representations, generalized symmetric groups, complex reflection groups, limit of characters, 20C25, 20F55, 40A30, 43A35
Based on the hereditary property from “mother groups” , , to their “child groups” , , 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 , and then of spin characters of the inductive limit groups . By further studying the heredity, we give the main kernel of the results for the child groups with .