Abstract
We consider a finite subgroup /spl Theta//sub n/ of the group O(N) of orthogonal matrices, where N=2/sup n/, n=1, 2, ... . This group was defined in [4] and we use it to construct spherical designs in the 2/sup n/-dimensional Euclidean space R/sup N/. We prove that representations /spl rho//sub 1/, /spl rho//sub 2/ and /spl rho//sub 3/ of the group /spl Theta//sub n/ on the spaces of harmonic polynomials of degrees 1, 2 and 3 respectively are irreducible. This together with the earlier results [1, 3] imply that the orbit /spl Theta//sub n,2/x of any initial point x on the unit sphere S/sub N-1/ is a 7-design in the Euclidean space of dimension 2/sup n/.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
