659 , 2017-10 , Osaka University and Osaka City University, Departments of Mathematics
This paper deals with necessary conditions for the existence of equivariant maps between the unit spheres of unitary representations of a cyclic p-group G. T. Bartsch gave a necessary condition for some unitary representations of G by using equivariant K-theory. We give two necessary conditions following Bartsch’s approach. One is a generalization of Bartsch’s result for any unitary representation of G which does not contain the trivial representation. The other is a stronger necessary condition for some special cases.