Pseudo unitary conformal groups and Clifford algebras for standard pseudo hermitian spaces

摘要

This paper, self-contained, deals with pseudo-unitary spin geometry. First, we present pseudo-unitary conformal structures over a 2n-dimensional complex manifold V and the corresponding projective quadrics $ ifmmodeexpandaftertildeelseexpandafter~fi{H}_{{p,q}} $ for standard pseudo-hermitian spaces H p,q . Then we develop a geometrical presentation of a compactification for pseudo-hermitian standard spaces in order to construct the pseudo-unitary conformal group of H p,q . We study the topology of the projective quadrics $ ifmmodeexpandaftertildeelseexpandafter~fi{H}_{{p,q}} $ and the “generators” of such projective quadrics. Then we define the space S of spinors canonically associated with the pseudo-hermitian scalar product of signature (2 n−1, 2 n−1). The spinorial group Spin U(p,q) is imbedded into SU(2 n−1, 2 n−1). At last, we study the natural imbeddings of the projective quadrics $ ifmmodeexpandaftertildeelseexpandafter~fi{H}_{{p,q}}. $