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Unitary Representations of Unitary Groups [PDF]
, 2013 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 ...
A. A. Kirillov +22 more
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The conformal characters [PDF]
Journal of High Energy Physics, 2018 We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules.
Antoine Bourget, Jan Troost
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European Physical Journal C: Particles and Fields, 2018 We discuss properties of fuzzy de Sitter space defined by means of algebra of the de Sitter group $$\text {SO}(1,4)$$ SO(1,4) in unitary irreducible representations.
Maja Burić +2 more
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Unitary Braid Representations with Finite Image [PDF]
Algebraic & Geometric Topology, 2008 We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.Comment: 17 ...
Bakalov +11 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
C Itzykson, M Nauenberg
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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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Boundary unitary representations-irreducibility and rigidity
Journal of Modern Dynamics, 2011 Let $M$ be compact negatively curved manifold, $Γ=π_1(M)$ and $\tilde{M}$ be its universal cover. Denote by $B =\partial \tilde{M}$ the geodesic boundary of $\tilde{M}$ and by $ν$ the Patterson-Sullivan measure on $X$. In this note we prove that the associated unitary representation of $Γ$ on $L^2(B,ν)$ is irreducible.
Uri Bader
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Transfer of Unitary Representations [PDF]
Asian Journal of Mathematics, 2004 In the present paper, the authors explain and give applications of the notion of transfer between real forms of a semi-simple Lie group \(G^{\mathbb C}\) over \(\mathbb C\), which first appeared in [\textit{N. R. Wallach}, Contemp. Math. 177, 181--216 (1994; Zbl 0833.22021)]. The main idea is that some representation of a real form of \(G^{\mathbb C}\)
Wallach, Nolan R., Zhu, Chen-Bo
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On families of twisted power partial isometries
Karpatsʹkì Matematičnì Publìkacìï, 2022 We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $\lambda_{ij}\in\mathbb C$, $|\lambda_{ij}|=1$.
V.L. Ostrovskyi +2 more
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Dyson’s classification and real division superalgebras
Journal of High Energy Physics, 2021 It is well-known that unitary irreducible representations of groups can be usefully classified in a 3-fold classification scheme: Real, Complex, Quaternionic.
Roman Geiko, Gregory W. Moore
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