In previous work, we associated to \(\text {SU(3)}\) , \(\textrm{G}_2\) , and \(\text {Spin(7)}\) -structures minimal left ideals for the Clifford algebras \(\mathbb {R}_{0,6},\mathbb {R}_{0,7}\) , and \(\mathbb {R}_{0,8}\) , respectively. In this paper, we continue to analyze the link between Berger’s classification theorem and the structure theorem of minimal left ideals for Clifford algebras of signature (p, q) by identifying \(\textrm{U}(n)\) -structures with minimal left ideals for Clifford algebras of various signatures via the induced Kahler polynomial \(P(\omega _{0})\) associated with the symplectic form \(\omega _{0}\) that defines the \(\textrm{U}(n)\) -structure as a stabilizer subgroup of \(\textrm{O}(n)\) .
