Which Group Structures on S3 have a maximal torus?

1978 ◽  
pp. 353-360 ◽  
Author(s):  
Charles A. McGibbon
Keyword(s):  
Maximal Torus ◽  
Group Structures

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
Author(s):  
George Kempf
Keyword(s):  
Irreducible Representation ◽  
General Formula ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Reductive Group ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Know How ◽  
Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

Rate Control of Helix Oscillation of Poly(arylacetylene)s Achieved by Design of Side-Group Structures

2021 ◽  
Author(s):  
Yasuteru Mawatari ◽  
Muneki Oouchi ◽  
Yoshiaki Yoshida ◽  
Toshifumi Hiraoki ◽  
Masayoshi Tabata
Keyword(s):  
Rate Control ◽  
Side Group ◽  
Group Structures

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

scholarly journals Orthogonal groups containing a given maximal torus

2003 ◽  
Vol 266 (1) ◽  
pp. 87-101 ◽  
Author(s):  
Rosali Brusamarello ◽  
Pascale Chuard-Koulmann ◽  
Jorge Morales
Keyword(s):  
Maximal Torus ◽  
Orthogonal Groups

scholarly journals Finite and infinite dimensional Lie group structures on Riordan groups

2017 ◽  
Vol 319 ◽  
pp. 522-566 ◽  
Author(s):  
Gi-Sang Cheon ◽  
Ana Luzón ◽  
Manuel A. Morón ◽  
L. Felipe Prieto-Martinez ◽  
Minho Song
Keyword(s):  
Lie Group ◽  
Infinite Dimensional ◽  
Infinite Dimensional Lie Group ◽  
Group Structures

scholarly journals Using Design-Based Research to Develop Meaningful Online Discussions in Undergraduate Field Experience Courses

2017 ◽  
Vol 18 (6) ◽  
Author(s):  
Carol Johnson ◽  
Laurie Hill ◽  
Jennifer Lock ◽  
Noha Altowairiki ◽  
Christopher Ostrowski ◽  
...  
Keyword(s):  
Deep Learning ◽  
Organizational Design ◽  
Field Experience ◽  
Online Discussion ◽  
Online Discussions ◽  
Task Completion ◽  
Discussion Forums ◽  
Design Based Research ◽  
Online Discussion Forums ◽  
Group Structures

<p class="3">From a design perspective, the intentionality of students to engage in surface or deep learning is often experienced through prescribed activities and learning tasks. Educators understand that meaningful learning can be furthered through the structural and organizational design of the online environment that motivates the student towards task completion. However, learning engagement is unique for each student. It is dependent on both how students learn and their intentions for learning. Based on this challenge, the design of online discussions becomes a pedagogical means in developing students’ intentionality for the adoption of strategies leading to deep learning. Through a Design-Based Research (DBR) approach, iterative design of online learning components for undergraduate field experience courses were studied. For this paper, the focus of the research is on examining factors that influenced deep and surface levels of learning in online discussion forums. The results indicate that design factors (i.e., student engagement, group structures, and organization) influence the nature and degree of deep learning. From the findings, two implications for practice are shared to inform the design and scaffolding of online discussion forums to foster deep approaches to student learning.</p>

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