Deformations of Irreducible Unitary Representations of the Discrete Series of Hermitian-Symmetric Simple Lie Groups in the Class of Pure Pseudo-Representations

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We prove that irreducible unitary representations of the discrete series of simple Hermitian-symmetric Lie groups can be continuously deformed in the class of pure unitary pseudo-representations (note that these representations cannot be continuously deformed in the class of unitary representations). We also briefly recall the main definitions and facts related to the notions of quasi-symmetry and pseudo-symmetry and to the realization of representations of the holomorphic discrete series of simple hermitian-symmetric Lie groups.