Quasi-regular Representations of Two-Step Nilmanifolds

2017 ◽  
pp. 137-155
Author(s):  
Amira Ghorbel ◽  
Hatem Hamrouni
Keyword(s):  
Regular Representations

scholarly journals Quantum Heisenberg group and algebra: Contraction, left and right regular representations

1995 ◽  
Vol 36 (3) ◽  
pp. 1404-1412 ◽  
Author(s):  
Demosthenes Ellinas ◽  
Jan Sobczyk
Keyword(s):  
Heisenberg Group ◽  
Regular Representations ◽  
Left And Right ◽  
And Algebra

scholarly journals Unitarization of the Horocyclic Radon Transform on Homogeneous Trees

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Francesca Bartolucci ◽  
Filippo De Mari ◽  
Matteo Monti
Keyword(s):  
Radon Transform ◽  
Homogeneous Tree ◽  
Homogeneous Trees ◽  
Regular Representations ◽  
Group Of Isometries

AbstractFollowing previous work in the continuous setup, we construct the unitarization of the horocyclic Radon transform on a homogeneous tree X and we show that it intertwines the quasi regular representations of the group of isometries of X on the tree itself and on the space of horocycles.

scholarly journals The Plancherel formula for the horocycle space and generalizations

1996 ◽  
Vol 61 (1) ◽  
pp. 42-56 ◽  
Author(s):  
Ronald L. Lipsman
Keyword(s):  
Harmonic Analysis ◽  
Regular Representation ◽  
Plancherel Formula ◽  
Intertwining Operators ◽  
Direct Integral ◽  
Regular Representations ◽  
Spectral Distributions ◽  
Theoretic Technique ◽  
Direct Integral Decomposition ◽  
Integral Decomposition

AbstractThe Plancherel formula for the horocycle space, and several generalizations, is derived within the framework of quasi-regular representations which have monomial spectrum. The proof uses only machinery from the Penney-Fujiwara distribution-theoretic technique; no special semisimple harmonic analysis is needed. The Plancherel formulas obtained include the spectral distributions and the intertwining operators that effect the direct integral decomposition of the quasi-regular representation.

Graphical Regular Representations of Non-Abelian Groups, II

1972 ◽  
Vol 24 (6) ◽  
pp. 1009-1018 ◽  
Author(s):  
Lewis A. Nowitz ◽  
Mark E. Watkins
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Regular Representation ◽  
Affirmative Answer ◽  
Roman Numeral ◽  
Regular Representations ◽  
Graphical Regular Representation ◽  
Bold Face

The present paper is a sequel to the previous paper bearing the same title by the same authors [3] and which will be hereafter designated by the bold-face Roman numeral I. Further results are obtained in determining whether a given finite non-abelian group G has a graphical regular representation. In particular, an affirmative answer will be given if (|G|, 6) = 1.Inasmuch as much of the machinery of I will be required in the proofs to be presented and a perusal of I is strongly recommended to set the stage and provide motivation for this paper, an independent and redundant introduction will be omitted in the interest of economy.

scholarly journals Chief Series and Right Regular Representations of Finite p-Groups

1988 ◽  
Vol 44 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Felix Leinen
Keyword(s):  
Regular Representation ◽  
Locally Finite ◽  
Regular Representations ◽  
Direct Limits ◽  
One To One ◽  
The Right

AbstractWe study the embeddings of a finite p-group U into Sylow p-subgroups of Sym (U) induced by the right regular representation p: U→ Sym(U). It turns out that there is a one-to-one correspondence between the chief series in U and the Sylow p-subgroups of Sym (U) containing Up. Here, the Sylow p-subgroup Pσ of Sym (U) correspoding to the chief series σ in U is characterized by the property that the intersections of Up with the terms of any chief series in Pσ form σp. Moreover, we see that p: U→ Pσ are precisely the kinds of embeddings used in a previous paper to construct the non-trivial countable algebraically closed locally finite p-groups as direct limits of finite p-groups.

Representations and cohomologies of regular Hom-pre-Lie algebras

2019 ◽  
Vol 19 (08) ◽  
pp. 2050149
Author(s):  
Shanshan Liu ◽  
Lina Song ◽  
Rong Tang
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Cohomology Theory ◽  
Trivial Representation ◽  
Linear Deformation ◽  
Dual Representations ◽  
Regular Representations ◽  
Equivalent Characterization ◽  
Tensor Representations

In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of regular Hom-pre-Lie algebras in terms of the cohomology theory of regular Hom-Lie algebras. As applications, we study linear deformations of regular Hom-pre-Lie algebras, which are characterized by the second cohomology groups of regular Hom-pre-Lie algebras with the coefficients in the regular representations. The notion of a Nijenhuis operator on a regular Hom-pre-Lie algebra is introduced which can generate a trivial linear deformation of a regular Hom-pre-Lie algebra. Finally, we introduce the notion of a Hessian structure on a regular Hom-pre-Lie algebra, which is a symmetric nondegenerate 2-cocycle with the coefficient in the trivial representation. We also introduce the notion of an [Formula: see text]-operator on a regular Hom-pre-Lie algebra, by which we give an equivalent characterization of a Hessian structure.

scholarly journals On the Haagerup and Kazhdan properties of R. Thompson’s groups

2019 ◽  
Vol 22 (5) ◽  
pp. 795-807 ◽  
Author(s):  
Arnaud Brothier ◽  
Vaughan F. R. Jones
Keyword(s):  
Commutator Subgroup ◽  
Invariant Vector ◽  
Haagerup Property ◽  
Thompson Groups ◽  
Thompson's Groups ◽  
Intermediate Subgroup ◽  
Regular Representations ◽  
Left Regular ◽  
Invariant Vectors ◽  
Property T

Abstract A machinery developed by the second author produces a rich family of unitary representations of the Thompson groups F, T and V. We use it to give direct proofs of two previously known results. First, we exhibit a unitary representation of V that has an almost invariant vector but no nonzero {[F,F]} -invariant vectors reproving and extending Reznikoff’s result that any intermediate subgroup between the commutator subgroup of F and V does not have Kazhdan’s property (T) (though Reznikoff proved it for subgroups of T). Second, we construct a one parameter family interpolating between the trivial and the left regular representations of V. We exhibit a net of coefficients for those representations which vanish at infinity on T and converge to 1 thus reproving that T has the Haagerup property after Farley who further proved that V has this property.

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