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Unitary Representations of Unitary Groups [PDF]
, 2014 In this paper we review and streamline some results of Kirillov, Olshanski and Pickrell on unitary representations of the unitary group $\U(\cH)$ of a real, complex or quaternionic separable Hilbert space and the subgroup $\U_\infty(\cH)$, consisting of those unitary operators $g$ for which $g - \1$ is compact.
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Endomorphisms of spaces of virtual vectors fixed by a discrete group
, 2015 Consider a unitary representation $\pi$ of a discrete group $G$, which, when restricted to an almost normal subgroup $\Gamma\subseteq G$, is of type II.
Radulescu, Florin
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Representations of Anisotropic Unitary Groups [PDF]
Transactions of the American Mathematical Society, 1988 Let S U ( f ) SU(f) be the special unitary group of an anisotropic hermitian form f f over a field k k . Assume f f represents only one norm class in k k . The representations α : S U
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Unitary representations of non-compact supergroups [PDF]
Communications in Mathematical Physics, 1983 Lie superalgebras have been studied as a model of the symmetries of elementary particles [e.g., \textit{J. Wess} and \textit{B. Zumino}, Supergauge transformations in four dimensions, Nucl. Phys. B 70, 39--50 (1974)], and as interesting mathematical objects in their own right [e.g. \textit{V. G. Kac}, Adv. Math. 26, 8--96 (1977; Zbl 0366.17012)].
Bars, I., Günaydin, M.
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Indefinite causal order strategy does not improve the estimation of group action [PDF]
QuantumWe consider estimation of unknown unitary operation when the set of possible unitary operations is given by a projective unitary representation of a compact group.
Masahito Hayashi
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Matrix Product Representation of Locality Preserving Unitaries [PDF]
, 2017 The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that are unitary ...
Bi, Feng +3 more
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Unitary Groups: Representations and Decompositions [PDF]
Reviews of Modern Physics, 1966 An elementary account is given of the representation theory for unitary groups. We review the basic definitions and the construction of irreducible representations using tensor methods, and indicate the connection to the infinitesimal approach. Special attention has been given to the detailed procedure to obtain Clebsch-Gordan series and to the problem
Itzykson, C., Nauenberg, M.
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Born's Rule From the Principle of Unitary Equivalence
, 2019 Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant.
Wallentin, Fritiof
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Unitary Representations of Oligomorphic Groups [PDF]
Geometric and Functional Analysis, 2012 Removed the requirement that an oligomorphic group be closed in Definition 1.2 in order to render Theorem 2.4 correct.
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On the image of the Lawrence-Krammer representation
, 2005 A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant ...
Budney, Ryan
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