The Genuine Omega-regular Unitary Dual of the Metaplectic Group

2012 ◽  
Vol 64 (3) ◽  
pp. 669-704
Author(s):  
Alessandra Pantano ◽  
Annegret Paul ◽  
Susana A. Salamanca-Riba
Keyword(s):  
Tensor Product ◽  
Unitary Representations ◽  
Dimensional Representation ◽  
Oscillator Representation ◽  
One Dimensional ◽  
Metaplectic Group ◽  
Unitary Dual ◽  
Cohomological Induction

Abstract We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator representation. Our main theorem asserts that this family exhausts the genuine omega-regular unitary dual of the metaplectic group.

scholarly journals On the Unitary Representations of the Braid Group B6

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1080
Author(s):  
Malak M. Dally ◽  
Mohammad N. Abdulrahim
Keyword(s):  
Braid Group ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Unitary Representations ◽  
Irreducible Representations ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Low Degree ◽  
Hermitian Positive Definite Matrix ◽  
Group B

We consider a non-abelian leakage-free qudit system that consists of two qubits each composed of three anyons. For this system, we need to have a non-abelian four dimensional unitary representation of the braid group B 6 to obtain a totally leakage-free braiding. The obtained representation is denoted by ρ . We first prove that ρ is irreducible. Next, we find the points y ∈ C * at which the representation ρ is equivalent to the tensor product of a one dimensional representation χ ( y ) and μ ^ 6 ( ± i ) , an irreducible four dimensional representation of the braid group B 6 . The representation μ ^ 6 ( ± i ) was constructed by E. Formanek to classify the irreducible representations of the braid group B n of low degree. Finally, we prove that the representation χ ( y ) ⊗ μ ^ 6 ( ± i ) is a unitary relative to a hermitian positive definite matrix.

scholarly journals Smooth representations of unit groups of split basic algebras over non-Archimedean local fields

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Carlos A. M. André ◽  
João Dias
Keyword(s):  
Local Field ◽  
Unit Group ◽  
Basic Algebra ◽  
Local Fields ◽  
Dimensional Representation ◽  
Smooth Representation ◽  
One Dimensional ◽  
Finite Dimensional

Abstract We consider smooth representations of the unit group G = A × G=\mathcal{A}^{\times} of a finite-dimensional split basic algebra 𝒜 over a non-Archimedean local field. In particular, we prove a version of Gutkin’s conjecture, namely, we prove that every irreducible smooth representation of 𝐺 is compactly induced by a one-dimensional representation of the unit group of some subalgebra of 𝒜. We also discuss admissibility and unitarisability of smooth representations of 𝐺.

scholarly journals An algorithm for delineating and extracting hillslopes and hillslope width functions from gridded elevation data

2011 ◽  
Vol 8 (5) ◽  
pp. 8865-8901
Author(s):  
P. Noel ◽  
A. N. Rousseau ◽  
C. Paniconi
Keyword(s):  
Three Dimensional ◽  
Rainfall Runoff ◽  
Dimensional Representation ◽  
New Approach ◽  
One Dimensional ◽  
Digital Elevation ◽  
Elevation Data ◽  
Average Profile ◽  
Elevation Model ◽  
Digital Elevation Model Resolution

Abstract. Subdivision of catchment into appropriate hydrological units is essential to represent rainfall-runoff processes in hydrological modelling. The commonest units used for this purpose are hillslopes (e.g. Fan and Bras, 1998; Troch et al., 2003). Hillslope width functions can therefore be utilised as one-dimensional representation of three-dimensional landscapes by introducing profile curvatures and plan shapes. An algorithm was developed to delineate and extract hillslopes and hillslope width functions by introducing a new approach to calculate an average profile curvature and plan shape. This allows the algorithm to be independent of digital elevation model resolution and to associate hillslopes to nine elementary landscapes according to Dikau (1989). This algortihm was tested on two flat and steep catchments of the province of Quebec, Canada. Results showed great area coverage for hillslope width function over individual hillslopes and entire watershed.

A CAD/CAM Representation Model Applied to Tolerance Transfer Methods

1998 ◽  
Author(s):  
Alain Desrochers
Keyword(s):  
Three Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Dimensional Tolerance ◽  
Representation Model ◽  
Three Dimensional Representation ◽  
Tolerance Chart ◽  
Cad Cam ◽  
Tolerance Charts

Abstract This paper presents the adaptation of tolerance transfer techniques to a model called TTRS for Technologically and Topologically Related Surfaces. According to this model, any three-dimensional part can be represented as a succession of surface associations forming a tree. Additional tolerancing information can be associated to each TTRS represented as a node on the tree. This information includes dimensional tolerances as well as tolerance chart values. Rules are then established to simulate tolerance chains or stack up along with tolerance charts directly from the graph. This way it becomes possible to combine traditional one dimensional tolerance transfer techniques with a powerful three-dimensional representation model providing high technological contents.

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

QUASI-EXACTLY SOLVABLE PROBLEMS AND SU(1,1) GROUP

1994 ◽  
Vol 09 (16) ◽  
pp. 1501-1505 ◽  
Author(s):  
O.B. ZASLAVSKII
Keyword(s):  
Lie Algebra ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Infinite Dimensional Representation

It is shown that the particular class of one-dimensional quasi-exactly solvable models can be constructed with the help of infinite-dimensional representation of Lie algebra. Hamiltonian of a system is expressed in terms of SU(1,1) generators.

scholarly journals A Two-Dimensional Genetic Algorithm and Its Application to Aircraft Scheduling Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Ming-Wen Tsai ◽  
Tzung-Pei Hong ◽  
Woo-Tsong Lin
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Scheduling Problem ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Time Table ◽  
Feasible Solutions ◽  
Crossover And Mutation ◽  
Airline Company

Genetic algorithms have become increasingly important for researchers in resolving difficult problems because they can provide feasible solutions in limited time. Using genetic algorithms to solve a problem involves first defining a representation that describes the problem states. Most previous studies have adopted one-dimensional representation. Some real problems are, however, naturally suitable to two-dimensional representation. Therefore, a two-dimensional encoding representation is designed and the traditional genetic algorithm is modified to fit the representation. Particularly, appropriate two-dimensional crossover and mutation operations are proposed to generate candidate chromosomes in the next generations. A two-dimensional repairing mechanism is also developed to adjust infeasible chromosomes to feasible ones. Finally, the proposed approach is used to solve the scheduling problem of assigning aircrafts to a time table in an airline company for demonstrating the effectiveness of the proposed genetic algorithm.

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