Self-adjoint elements in the pseudo-unitary group U(p,p)

The pseudo-unitary group U(p,q) of signature (p,q) is the group of matrices that preserve the indefinite pseudo-Euclidean metric on the vector space Cp,q. The goal of this paper is to describe the set Us(p,p) of Hermitian, or, self-adjoint elements in U(p,p).