CLASSICAL METHOD OF CONSTRUCTING A COMPLETE SET OFIRREDUCIBLE REPRESENTATIONS OF SEMIDIRECT PRODUCT OF ACOMPACT GROUP WITH A FINITE GROUP
Takeshi Hirai
Abstract: Let be a group of semidirect product of compact and finite. For an
irreducible representation (= IR) of , let be the stationary subgroup in of the
equivalence class . Intertwining operators between and
gives in general a spin (= projective) representation of , which is lifted up to a linear
representation of a covering group of . Put , and take a
spin representation of corresponding to the factor set inverse to that of
, and put . We give a simple proof that
is irreducible and that any IR of is equivalent to some of .
Keywords and phrases: Semidirect product group, construction of irreducible
representations, projective representation, finite group and compact group.