INVARIANT CR MAPPINGS BETWEEN HYPERQUADRICS

摘要

We analyze a canonical construction of group-invariant CR Mappings between hyperquadrics due to D'Angelo. Given source hyperquadric of Q(1, 1), we determine the signature of the target hyperquadric for all finite subgroups of SU(1,1). We also extend combinatorial results proven by Loehr, Warrington, and Wilf on determinants of sparse circulant determinants. We apply these results to study CR mappings invariant under finite subgroups of U(1,1).