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A Weight Theory for Unitary Representations
Canadian Journal of Mathematics, 1966Over a field of characteristic 0 certain of the simple Lie algebras have a root theory, namely those called “split” in Jacobson's book (3). We shall assume some familiarity with the subject matter of this book. Then the finite-dimensional representations of these Lie algebras have a weight theory.
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On Unitary Representations of the Inhomogeneous Lorentz Group
Nuclear Physics B - Proceedings Supplements, 1939It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state.
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On pseudo-unitary representations
Czechoslovak Journal of Physics, 1987The structure of representations of a group on a finite dimensional complex vector space with a non-degenerate invariant (indefinite) inner product is analysed in terms of layers of Gupta-Bleuler triplets.
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Deep random walk of unitary invariance for large-scale data representation
Information Sciences, 2021Shiping Wang, Zheyi Chen, William Zhu
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Reproducing Kernel Hilbert Space Associated with a Unitary Representation of a Groupoid
Complex Analysis and Operator Theory, 2021Monika Drewnik +2 more
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Classical dynamics from a unitary representation of the Galilei group
Annals of Physics, 2020A D Bermúdez Manjarres +2 more
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Positive Unitary Representations
2000In this chapter we collect some preliminaries in abstract Hilbert analysis which will be used in subsequent chapters.
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