Equivariant maps between representation spheres of cyclic ${p}$-groups

Abstract

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.