Invariant CR mappings between hyperquadrics

Abstract

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.

Constructing group-invariant CR mappings

“…Finally, we have focused on sphere mappings, but a natural extension is to generalize to hyperquadric mappings (see [2,3,22,23] for work in this direction).…”

“…For any fixed-point-free, finite subgroup , D'Angelo gives a construction of a canonical group-invariant CR mapping from a sphere to a hyperquadric. In general, it is difficult to determine the exact target hyperquadric (see [20,21,23] for more in this direction). However, in the case of an admissible subgroup, the target is a sphere.…”

Constructing Group-Invariant CR Mappings

“…For any fixed-point-free, finite subgroup Γ, D'Angelo gives a construction of a canonical group-invariant CR mapping from a sphere to a hyperquadric. In general, it is difficult to determine the exact target hyperquadric (see [20,21,23] for more in this direction). However, in the case of an admissible subgroup, the target is a sphere.…”