Représentations irréductibles bornées des groupes de Lie exponentiels

2001 ◽  
Vol 53 (5) ◽  
pp. 944-978 ◽  
Author(s):  
J. Ludwig ◽  
C. Molitor-Braun
Keyword(s):  
Banach Space ◽  
Irreducible Representation ◽  
Lie Group ◽  
Simple Extension ◽  
Induced Representations ◽  
New Type ◽  
Exponential Lie Group

AbstractLet G be a solvable exponential Lie group. We characterize all the continuous topologically irreducible bounded representations (T, ) of G on a Banach space by giving a G-orbit in n* (n being the nilradical of g), a topologically irreducible representation of L1(ℝn, ω), for a certain weight ω and a certain n ∈ ℕ, and a topologically simple extension norm. If G is not symmetric, i.e., if the weight ω is exponential, we get a new type of representations which are fundamentally different from the induced representations.

scholarly journals Analytic vectors in continuousp-adic representations

2009 ◽  
Vol 145 (1) ◽  
pp. 247-270 ◽  
Author(s):  
Tobias Schmidt
Keyword(s):  
Banach Space ◽  
Lie Group ◽  
The Other ◽  
Induced Representations ◽  
Faithful Functor ◽  
Other Hand ◽  
Derived Functors

AbstractGiven a compactp-adic Lie groupGover a finite unramified extensionL/ℚplet GL/ℚpbe the product over all Galois conjugates ofG. We construct an exact and faithful functor from admissibleG-Banach space representations to admissible locallyL-analyticGL/ℚp-representations that coincides with passage to analytic vectors in the caseL=ℚp. On the other hand, we study the functor ‘passage to analytic vectors’ and its derived functors over general basefields. As an application we compute the higher analytic vectors in certain locally analytic induced representations.

scholarly journals Correction: Çakmak, A. New Type Direction Curves in 3-Dimensional Compact Lie Group Symmetry 2019, 11, 387

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 284
Author(s):  
Ali Çakmak
Keyword(s):  
Lie Group ◽  
Group Symmetry ◽  
Compact Lie Group ◽  
3 Dimensional ◽  
New Type ◽  
Lie Group Symmetry

The authors wish to make the following corrections to their paper [...]

Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Atlas of DOF Characteristic Matrix

2006 ◽  
Author(s):  
Jingjun Yu ◽  
Jian S. Dai ◽  
Xin-Jun Liu ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
System Theory ◽  
Lie Group ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Complete Classification ◽  
Characteristic Matrix ◽  
Type Synthesis ◽  
Lie Group Theory ◽  
Low Degree ◽  
New Type

Low-degree-of-freedom (Low-DOF) parallel manipulators (PMs) have drawn extensive interest, particularly in type synthesis in which two main approaches were established in the reciprocal screw system theory and Lie group theory. This paper aims at proposing a new type synthesis method to complementing the above methods. For this purpose, the concept of the DOF characteristic matrix, originated from displacement subgroup and displacement submanifold, is proposed. A new but general approach based on the atlas of DOF Characteristic Matrix is addressed for both exhaustive classification and type synthesis of low-DOF PMs. Compared to the method based on Lie group, the proposed approach is prone to construct an orthogonal structure and easy to realize the complete classification and exhaustive enumeration of a class of low-DOF PM. In order to verify the effectiveness of the proposed method, type synthesis of Translational PMs (TPMs) particularly in ones with an orthogonal structure is performed, resulting in some novel orthogonal TPMs.

Infinitesimal Generators on the Quantum Group SUq(2)

1998 ◽  
Vol 01 (04) ◽  
pp. 573-598 ◽  
Author(s):  
Michael Schürmann ◽  
Michael Skeide
Keyword(s):  
Irreducible Representation ◽  
Quantum Group ◽  
Lie Group ◽  
Lévy Processes ◽  
Levy Processes ◽  
Infinite Dimensional ◽  
Infinitesimal Generators ◽  
Dimensional Irreducible Representation

Quantum Lévy processes on a quantum group are, like classical Lévy processes with values in a Lie group, classified by their infinitesimal generators. We derive a formula for the infinitesimal generators on the quantum group SU q(2) and decompose them in terms of an infinite-dimensional irreducible representation and of characters. Thus we obtain a quantum Lévy–Khintchine formula.

Local Central Λ(p) Dual Objects

1977 ◽  
Vol 20 (4) ◽  
pp. 515-515
Author(s):  
Willard A. Parker
Keyword(s):  
Irreducible Representation ◽  
Compact Group ◽  
Lie Group ◽  
Compact Lie Group ◽  
Irreducible Characters ◽  
Dual Object

The dual object T of a compact group is called a local central A(p) set if there is a constant K such that ‖X‖P < K ‖X‖1 for all irreducible characters X of G. For each γ∊Γ, Dr is an irreducible representation of G of dimension dγ. Several authors [1, 2, 3, 4] have observed that Γ is a local central Λ(p) set for p<l provided sup{dγ:γ∊Γ}>∞, and some of them [2, 3] conjectured the converse. Cecchini [1] showed that Γ is not a local central Λ(4) set if G is a compact Lie group.

Basis states for equivalent electrons. II. States for the Lie group Sp(4l + 2)

1980 ◽  
Vol 58 (12) ◽  
pp. 1724-1728
Author(s):  
William R. Ross
Keyword(s):  
Angular Momentum ◽  
Irreducible Representation ◽  
Orbital Angular Momentum ◽  
Lie Group ◽  
Total Spin ◽  
Irreducible Representations ◽  
Total Orbital Angular Momentum ◽  
Intermediate Group ◽  
Slater Basis

The Slater basis states for N equivalent electrons form the basis for the irreducible representation (1N) of the Lie group U(4l + 2). States which are eigenfunctions of the total spin and total orbital angular momentum form the basis for irreducible representations of SO(3) × SU(2). In this paper the intermediate group Sp(4l + 2) is studied. The basis states for irreducible representations of Sp(4l + 2) are expressed in terms of the Slater basis states.

Basis states for equivalent electrons. I. States for the Lie group U(2l + 1) × SU(2)

1980 ◽  
Vol 58 (12) ◽  
pp. 1718-1723
Author(s):  
William R. Ross
Keyword(s):  
Irreducible Representation ◽  
Lie Group ◽  
Spin Operator ◽  
Total Spin ◽  
Slater Basis

The antisymmetric Slater basis states for N equivalent electrons form the basis for an irreducible representation of U(4l + 2). When we consider the subgroup U(2l + 1) × SU(2) we obtain states which are eigenstates of the total spin operator. The basis states for the irreducible representation of U(2l + 1) × SU(2) are expressed in terms of the Slater basis states. General expressions are obtained which can easily be applied regardless of the number of electrons, the value of l, or the irreducible representation that is considered.

On Asymptotic Behavior of Induced Representations

1982 ◽  
Vol 34 (1) ◽  
pp. 220-232 ◽  
Author(s):  
Larry Baggett ◽  
Keith F. Taylor
Keyword(s):  
Asymptotic Behavior ◽  
Unitary Representation ◽  
Lie Group ◽  
Closed Subgroup ◽  
List Type ◽  
Connected Component ◽  
Induced Representation ◽  
Induced Representations ◽  
Diagonal Subgroup ◽  
Connected Lie Group

This paper is devoted to the proof of the following theorem.THEOREM 1.1. Let H be a closed subgroup of a connected Lie group G, let N denote the largest (closed) subgroup of H which is normal in all of G, and suppose that π is a unitary representation of H whose restriction to N is a multiple of a character χ of N. Then every matrix coefficient of the induced representation Uπ vanishes at infinity modulo the kernel of Uπ providing that the following two conditions hold:i) N is almost-connected (finite modulo its connected component).ii) The subgroup Hk is “regularly related” to the diagonal subgroup D in Gk for at least one integer k ≧ k0 where k0 is determined by G and H.

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