We formulate the notion of parity for the periodic XXZ spin chain within the Quantum Inverse Scattering Method. We also propose an expression for the eigenvalues of the charge conjugation operator. We use these discrete symmetries to help classify low-lying Sz = 0 states in the critical regime, and we give a direct computation of the S matrix.

Let η be a Real bundle, in the sense of Atiyah, over a space X. This is a complex vector bundle together with an involution which is compatible with complex conjugation. We use the fact that BU has a canonical structure of a conjugation space, as defined by Hausmann, Holm, and Puppe, to construct equivariant Chern classes in certain equivariant cohomology groups of X with twisted integer coeffi...

The notions of rank and conjugation are developed in the context of a second Frobenius representation of an overpartition. Some identities for overpartitions that are invariant under this conjugation are presented.