Branching rules and even-dimensional rotation groups SO_2k

Abstract

Unambiguous methods are developed for calculating branching rules for the classical subgroups of the even-dimensional rotation group SO2k. Complete results are given for the subgroups SUk*U1, SO2k-2*U1, SO2p*SO2q and SO2p+1*SO2q+1. A number of examples relevant to problems in supergravity and unification theories are given. A complete resolution of the antisymmetric powers of the basic spinor irrep of SO10 is given and the results extended to SO11.