Irreducible Representations of Special Groups

1996 ◽  
pp. 87-125
Author(s):  
Wolfgang Ludwig ◽  
Claus Falter
Keyword(s):  
Irreducible Representations ◽  
Special Groups

An Intuitive Method for the Determination of Crystal-Field Parameters in Laser Crystals

1993 ◽  
Vol 329 ◽  
Author(s):  
Frederick G. Anderson ◽  
H. Weidner ◽  
P. L. Summers ◽  
R. E. Peale ◽  
B. H. T. Chai
Keyword(s):  
Crystal Field ◽  
Irreducible Representations ◽  
Laser Crystals ◽  
Intuitive Method ◽  
Crystal Field Parameters ◽  
Intuitive Interpretation

AbstractExpanding the crystal field in terms of operators that transform as the irreducible representations of the Td group leads to an intuitive interpretation of the crystal-field parameters. We apply this method to the crystal field experienced by Nd3+ dopants in the laser crystals YLiF4, YVO4, and KLiYF5.

Creative Methodologies of Da’wah Through Different Phases of a Human’s Life (Metodologi Dakwah Secara Kreatif Mengikut Fasa Kehidupan Manusia)

2018 ◽  
Vol 15 (1) ◽  
pp. 271-293
Author(s):  
Maulana Akbar Shah @ U Tun Aung
Keyword(s):  
Married Couples ◽  
Special Group ◽  
Target Groups ◽  
New Born ◽  
Special Groups ◽  
Pregnant Mothers ◽  
Do So

Abstract In addition to compliance with the five pillars of Islam, Da’wah Islamiyyah is an indispensable act for Muslims who view their life missions as to propagate Islam. The act of da’wah is a mission only undertaken by those who are selected to do so, as Allah SWT said: “You are the best of peoples, taken out for mankind, you enjoin what is right, forbid what is wrong…,” (Al-Qur’an, Al- `Imran, 3:110). The phrase “you are taken out for mankind” is a very clear phrase which refers to a special group. Many du’at propagate Islam through regular procedures. In this contemporary day and age, it would be more successful if creative da’wah methodologies are used to special groups where special talent is required. Examples of these special target groups are individuals such as [1] pregnant mothers, [2] mothers of new born babies, [3] parents of toddlers, [4] parents of children [5] youth, teenagers and adolescents, [6] married couples, [7] elderly or aged individuals and [8] non-Muslims.  They are good targets to promote Islam. Thus, du’at must have special talents and knowledge to do so. In this regard, du’at must be equipped with exceptional knowledge of the target groups to propagate Islam effectively. The present paper attempts to highlight the distinctive natures of the above mentioned categories of individuals and explores how du’at should approach them when he or she encounters them for the purpose of promoting Islam.        Keywords: Call to Islam, Da’wah Islamiyyah, creative da’wah, creative da’ie, enjoin good, forbid evil.   Abstrak Selain mematuhi 5 rukun Islam, dakwah Islamiyyah tidak dapat diasingkan daripada seseorang Muslim yang bermatlamat untuk menyebarkan ajaran Islam. Berdakwah adalah suatu tugas yang hanya dijalankan oleh mereka yang terpilih. Seperti yang diwahyukan oleh Allah SWT “Kamu adalah sebaik-baik umat yang dilahirkan bagi umat manusia, kerana kamu menyuruh berbuat segala perkara yang baik dan melarang daripada segala perkara yang buruk dan keji...” (Al-Quran, Al-Imran, 3:110). Frasa “umat yang dilahirkan bagi umat manusia”  jelas dinyatakan di mana ia merujuk kepada satu golongan yang istimewa. Kebanyakan pendakwah menyebarkan Islam melalui metodologi yang sudah menjadi kebiasaan. Bagaimanapun, pada zaman ini, pendakwahan akan lebih berjaya jika kaedah yang kreatif digunakan kepada beberapa golongan yang tertentu. Antara contoh golongan yang dimaksudkan adalah [1] wanita yang mengandung, [2] ibu kepada bayi yang baru lahir, [3] ibu bapa kepada anak-anak kecil, [4] ibu bapa kepada kanak-kanak, [5] golongan belia dan remaja, [6] pasangan suami isteri, [7] warga emas, dan [8] golongan bukan Islam. Mereka merupakan sasaran yang sempurna untuk mempelajari Islam. Oleh hal demikian, para pendakwah mesti mempunyai bakat yang istimewa dan ilmu yang mencukupi untuk berdakwah. Para pendakwah juga harus memahami kumpulan sasaran dengan menyeluruh supaya penyebaran ajaran Islam akan lebih berkesan. Tujuan penulisan ini adalah untuk menggariskan sifat unik golongan yang dinyatakan di atas dan menerokai bagaimana para pendakwah harus mendekati mereka dengan niat untuk menyebarkan Islam.   Kata Kunci: Panggilan kepada Islam, dakwah Islamiyyah, dakwah kreatif, da’ie kreatif, menyuruh kepada kebaikan, menghalang daripada kejahatan.  

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.

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