Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$

Corina Ciobotaru

doi:10.7146/math.scand.a-114722

Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-114722 ◽

2019 ◽

Vol 125 (1) ◽

pp. 113-134

Author(s):

Corina Ciobotaru

Keyword(s):

Unitary Representations ◽

Universal Group

We prove that all parabolically induced unitary representations of the Burger-Mozes universal group $U(F)^{+}$, with $F$ being primitive, are $C_0$. This generalizes the same well-known result for the universal group $U(F)^{+}$, when $F$ is $2$-transitive.

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Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

Journal of High Energy Physics ◽

10.1007/jhep03(2021)261 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Nadav Drukker ◽

Malte Probst ◽

Maxime Trépanier

Keyword(s):

Stress Tensor ◽

Unitary Representations ◽

Point Function ◽

Displacement Operator ◽

Expectation Value ◽

Operator Expansion ◽

Bulk Stress ◽

Defect Operator ◽

Tensor Multiplet

Abstract Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

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Heisenberg–Weyl Groups and Generalized Hermite Functions

Symmetry ◽

10.3390/sym13061060 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1060

Author(s):

Enrico Celeghini ◽

Manuel Gadella ◽

Mariano A. del del Olmo

Keyword(s):

Hilbert Space ◽

Fourier Transform ◽

Heisenberg Group ◽

Real Line ◽

Hermite Functions ◽

Unitary Representations ◽

Weyl Groups ◽

The Real ◽

Symmetry Properties ◽

The Fourier Transform

We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is, in some sense, shared by these “generalized Hermite functions”. The construction of these new bases is grounded on some symmetry properties of the real line under translations, dilations and reflexions as well as certain properties of the Fourier transform. We show how these generalized Hermite functions are transformed under the unitary representations of a series of groups, including the Weyl–Heisenberg group and some of their extensions.

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On infinite dimensional unitary representations of certain discrete groups

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/03320191 ◽

1981 ◽

Vol 33 (2) ◽

pp. 191-202

Author(s):

Yoshiyuki SATO

Keyword(s):

Unitary Representations ◽

Discrete Groups ◽

Infinite Dimensional

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On the unitary representations of exponential groups

Journal of Functional Analysis ◽

10.1016/0022-1236(68)90026-8 ◽

1968 ◽

Vol 2 (1) ◽

pp. 73-113 ◽

Cited By ~ 28

Author(s):

L Pukanszky

Keyword(s):

Unitary Representations

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IMBEDDING OF A GROUP OF MEASURE-PRESERVING DIFFEOMORPHISMS INTO A SEMIDIRECT PRODUCT AND ITS UNITARY REPRESENTATIONS

Mathematics of the USSR-Sbornik ◽

10.1070/sm1982v041n01abeh002221 ◽

1982 ◽

Vol 41 (1) ◽

pp. 67-81

Author(s):

R S Ismagilov

Keyword(s):

Semidirect Product ◽

Unitary Representations

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Branching laws of unitary representations associated to minimal elliptic orbits for indefinite orthogonal group O(p,q)

Advances in Mathematics ◽

10.1016/j.aim.2021.107862 ◽

2021 ◽

Vol 388 ◽

pp. 107862

Author(s):

Toshiyuki Kobayashi

Keyword(s):

Orthogonal Group ◽

Unitary Representations ◽

Branching Laws ◽

Elliptic Orbits

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On a construction of unitary cocycles and the representation theory of amenable groups

Ergodic Theory and Dynamical Systems ◽

10.1017/s014338570000184x ◽

1983 ◽

Vol 3 (1) ◽

pp. 129-133 ◽

Cited By ~ 1

Author(s):

Colin E. Sutherland

Keyword(s):

Representation Theory ◽

Probability Space ◽

Amenable Group ◽

Unitary Representations ◽

Intertwining Operators ◽

Type I ◽

Amenable Groups

AbstractIf K is a countable amenable group acting freely and ergodically on a probability space (Γ, μ), and G is an arbitrary countable amenable group, we construct an injection of the space of unitary representations of G into the space of unitary 1-cocyles for K on (Γ, μ); this injection preserves intertwining operators. We apply this to show that for many of the standard non-type-I amenable groups H, the representation theory of H contains that of every countable amenable group.

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