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This lecture covers the concept of Poincaré irreducible representations, focusing on the Little Group subgroup and induced representation. It explores the properties of Poincaré irreps, the subgroup leaving a given momentum invariant, and the induced representation construction. The lecture delves into the action of the Little Group on momentum eigenstates and the determination of states through boosting. It also discusses the standard basis choice for eigenvalues and the transformation properties under Lorentz transformations.