scholarly journals Crystal Rules for $(\ell,0)$-JM Partitions

10.37236/391 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Chris Berg
Keyword(s):  
Hecke Algebra ◽  
Analogous Condition ◽  
Specht Module ◽  
Root Of Unity ◽  
New Interpretation

Vazirani and the author [Electron. J. Combin., 15 (1) (2008), R130] gave a new interpretation of what we called $\ell$-partitions, also known as $(\ell,0)$-Carter partitions. The primary interpretation of such a partition $\lambda$ is that it corresponds to a Specht module $S^{\lambda}$ which remains irreducible over the finite Hecke algebra $H_n(q)$ when $q$ is specialized to a primitive $\ell^{th}$ root of unity. To accomplish this we relied heavily on the description of such a partition in terms of its hook lengths, a condition provided by James and Mathas. In this paper, I use a new description of the crystal $reg_\ell$ which helps extend previous results to all $(\ell,0)$-JM partitions (similar to $(\ell,0)$-Carter partitions, but not necessarily $\ell$-regular), by using an analogous condition for hook lengths which was proven by work of Lyle and Fayers.

scholarly journals $(\ell, 0)$-Carter Partitions and their crystal theoretic interpretation

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Chris Berg ◽  
Monica Vazirani
Keyword(s):  
Hecke Algebra ◽  
Specht Module ◽  
Regular Partition ◽  
Basic Representation ◽  
Crystal Graph ◽  
Generating Series ◽  
International Audience ◽  
The One ◽  
Regular Partitions ◽  
Nous Utilisons

International audience In this paper we give an alternate combinatorial description of the "$(\ell,0)$-Carter partitions''. Our main theorem is the equivalence of our combinatoric and the one introduced by James and Mathas ($\textit{A q-analogue of the Jantzen-Schaper theorem}$). The condition of being an $(\ell,0)$-Carter partition is fundamentally related to the hook lengths of the partition. The representation-theoretic significance of their combinatoric on an $\ell$-regular partition is that it indicates the irreducibility of the corresponding Specht module over the finite Hecke algebra. We use our result to find a generating series which counts the number of such partitions, with respect to the statistic of a partition's first part. We then apply our description of these partitions to the crystal graph $B(\Lambda_0)$ of the basic representation of $\widehat{\mathfrak{sl}_{\ell}}$, whose nodes are labeled by $\ell$-regular partitions. Here we give a fairly simple crystal-theoretic rule which generates all $(\ell,0)$-Carter partitions in the graph of $B(\Lambda_0)$. Dans cet article, nous donnons une description combinatoire alternative des partitions "$(\ell,0)$-Carter". Notre théorème principal est une équivalence entre notre combinatoire et celle introduite par James et Mathas ($\textit{A q-analogue of the Jantzen-Schaper theorem}$). La propriété $(\ell,0)$-Carter est fondamentalement liée aux longueurs des équerres de la partition. En terme de théorie des représentations, leur combinatoire pour une partition $\ell$-régulière permet de déterminer l'irréducibilité du module de Specht spécialisé sur l’algèbre de Hecke finie. Nous utilisons notre résultat pour déterminer leur série génératrice en fonction de la taille de la première part. Nous utilisons ensuite notre description de ces partitions au graphe cristallin $B(\Lambda _0)$ de la représentation basique de $\widehat{\mathfrak{sl}_{\ell}}$, dont les nœuds sont étiquetés par les partitions $\ell$-régulières. Nous donnons une règle cristalline relativement simple permettant d'engendrer toutes les partitions $\ell$-régulières $(\ell,0)$-Carter dans le graphe de $B(\Lambda _0)$.

scholarly journals $(\ell,0)$-Carter Partitions, their Crystal-Theoretic Behavior and Generating Function

10.37236/854 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Chris Berg ◽  
Monica Vazirani
Keyword(s):  
Symmetric Group ◽  
Generating Function ◽  
Hecke Algebra ◽  
Specht Module ◽  
Combinatorial Description ◽  
Basic Representation ◽  
Crystal Graph ◽  
Generating Series ◽  
The One ◽  
Regular Partitions

In this paper we give an alternate combinatorial description of the "$(\ell,0)$-Carter partitions". The representation-theoretic significance of these partitions is that they indicate the irreducibility of the corresponding specialized Specht module over the Hecke algebra of the symmetric group. Our main theorem is the equivalence of our combinatoric and the one introduced by James and Mathas, which is in terms of hook lengths. We use our result to find a generating series which counts such partitions, with respect to the statistic of a partition's first part. We then apply our description of these partitions to the crystal graph $B(\Lambda_0)$ of the basic representation of $\widehat{{sl}_{\ell}}$, whose nodes are labeled by $\ell$-regular partitions. Here we give a fairly simple crystal-theoretic rule which generates all $(\ell,0)$-Carter partitions in the graph $B(\Lambda_0)$.

scholarly journals On C-Bases, Partition Pairs and Filtrations for Induced or Restricted Specht Modules

2019 ◽  
Vol 26 (01) ◽  
pp. 161-180
Author(s):  
Christos A. Pallikaros
Keyword(s):  
Symmetric Group ◽  
Hecke Algebra ◽  
Specht Module ◽  
Specht Modules

We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = ℤ[q1/2, q−1/2], where q is an indeterminate) using C-bases for these modules. Moreover, we provide a link between a certain C-basis for the induced Specht module and the notion of pairs of partitions.

ON SCHUR-WEYL DUALITY, An HECKE ALGEBRAS AND QUANTUM sl(N) ON $\otimes^{n+1}{\mathbb C}^N$

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 645-673 ◽  
Author(s):  
PAUL PURDON MARTIN
Keyword(s):  
Hecke Algebras ◽  
Hecke Algebra ◽  
Model Representation ◽  
Complete Analysis ◽  
Vertex Model ◽  
Algebraic Structures ◽  
Root Of Unity ◽  
Weyl Duality

We prove that an N-state vertex model representation of the An Hecke algebra quotient NHn(q) is faithful for all q. We use the result to examine the indecomposable content of these representations, and hence the structure of the centraliser algebra, which is generically a quotient of Uqsl(N), at q a root of unity. We achieve a complete analysis in the case N=2, finding a number of Morita self-dual algebraic structures.

Esotericism and the “Coded Word” in Mormonism

2011 ◽  
Vol 2 (1) ◽  
pp. 29-54
Author(s):  
Clyde Forsberg Jr.
Keyword(s):  
Popular Religion ◽  
Latter Day Saints ◽  
Social Commentary ◽  
Joseph Smith ◽  
Playing Field ◽  
Book Of Mormon ◽  
Divine Inspiration ◽  
History Of ◽  
New Interpretation ◽  
New Religion

In the history of American popular religion, the Latter-day Saints, or Mormons, have undergone a series of paradigmatic shifts in order to join the Christian mainstream, abandoning such controversial core doctrines and institutions as polygamy and the political kingdom of God. Mormon historians have played an important role in this metamorphosis, employing a version (if not perversion) of the Church-Sect Dichotomy to change the past in order to control the future, arguing, in effect, that founder Joseph Smith Jr’s erstwhile magical beliefs and practices gave way to a more “mature” and bible-based self-understanding which is then said to best describe the religion that he founded in 1830. However, an “esoteric approach” as Faivre and Hanegraaff understand the term has much to offer the study of Mormonism as an old, new religion and the basis for a more even methodological playing field and new interpretation of Mormonism as equally magical (Masonic) and biblical (Evangelical) despite appearances. This article will focus on early Mormonism’s fascination with and employment of ciphers, or “the coded word,” essential to such foundation texts as the Book of Mormon and “Book of Abraham,” as well as the somewhat contradictory, albeit colonial understanding of African character and destiny in these two hermetic works of divine inspiration and social commentary in the Latter-day Saint canonical tradition.

BKR (BADAN KEAMANAN RAKYAT): Cikal Bakal Tentara Indonesia?

Metahumaniora ◽  
2018 ◽  
Vol 8 (3) ◽  
pp. 389
Author(s):  
Widyo Nugrahanto
Keyword(s):  
Armed Forces ◽  
Civil Defense ◽  
The Other ◽  
Main Subject ◽  
Japanese Occupation ◽  
Historical Method ◽  
New Interpretation

AbstrakPenelitian ini berjudul BKR (Badan Kemanan Rakyat):Cikal Bakal Tentara Indonesia?!. Penelitian ini merupakan interpretasi baru tentang cikal bakal TNI, yang umumnya banyak merujuk pada PETA (Pembela Tanah Air). Metode penelitian yang digunakan adalah Metode Sejarah.Metode Sejarah memiliki empat tahapan yaitu Heuristik, Kritik, Interpretasi dan Historiografi.Sumber-sumber penelitian ini menggunakan koran-koran sezaman, majalah sezaman, dan buku. BKR dianggap sebagai cikal bakal TNI didasarkan beberapa sebab. Pertama, atas dasar legalitas formal, PETA telah dibubarkan sehingga BKR adalah satuan militer yang pertama kali dibentuk setelah Indonesia merdeka. BKR selanjutnya melahirkan pembentukan TKR (Tentara Keamanan Rakyat), TKR (Tentara Keselamatan Rakyat), TRI (Tentara Republik Indonesia) dan TNI (Tentara Nasional Indonesia). Kedua, jika PETA dianggap sebagai cikal bakal TNI, maka KNIL dan beberapa satuan keprajuritan diabaikan. Padahal, beberapa bekas perwira KNIL memiliki peran penting di tubuh BKR hingga TNI.Kata kunci: BKR, Tentara, TNIAbstractThe main subject this study is BKR – Indonesian civil defense corps – as origin of Indonesian Military. This study is new interpretation about the origin of TNI (Indonesian National Armed Forces) now. Many opinion refer to PETA as civil defense corps in Japanese occupation era. Study emlpoys a Historical Method, which consists of four stage: Heuristic, Critic, Interpretation, Historiography. The study utilize some sources such as newspaper, magazine, and book. Main finding of this study is PETA had dispersed as legality and formally and BKR was formed as the firts corps after Independence of Indonesia. Futhermore, BKR changed to TKR (Tentara Keamanan Rakyat), TKR (Tentara Keselamatan Rakyat), TRI (Tentara Republik Indonesia) until TNI (Tentara Nasional Indonesia). If PETA is considered as origins of Indonesian Military, then it ignore KNIL – a colonial armed forces – and the other defence corps. Even though the eks KNIL’s officer have important role in military managenment of BKR until TNI.Keywords: BKR, Military, TNI

BKR (BADAN KEAMANAN RAKYAT): Cikal Bakal Tentara Indonesia?

Metahumaniora ◽  
2018 ◽  
Vol 8 (3) ◽  
pp. 389
Author(s):  
Widyo Nugrahanto
Keyword(s):  
Armed Forces ◽  
Civil Defense ◽  
The Other ◽  
Main Subject ◽  
Japanese Occupation ◽  
Historical Method ◽  
New Interpretation

AbstrakPenelitian ini berjudul BKR (Badan Kemanan Rakyat):Cikal Bakal Tentara Indonesia?!. Penelitian ini merupakan interpretasi baru tentang cikal bakal TNI, yang umumnya banyak merujuk pada PETA (Pembela Tanah Air). Metode penelitian yang digunakan adalah Metode Sejarah.Metode Sejarah memiliki empat tahapan yaitu Heuristik, Kritik, Interpretasi dan Historiografi.Sumber-sumber penelitian ini menggunakan koran-koran sezaman, majalah sezaman, dan buku. BKR dianggap sebagai cikal bakal TNI didasarkan beberapa sebab. Pertama, atas dasar legalitas formal, PETA telah dibubarkan sehingga BKR adalah satuan militer yang pertama kali dibentuk setelah Indonesia merdeka. BKR selanjutnya melahirkan pembentukan TKR (Tentara Keamanan Rakyat), TKR (Tentara Keselamatan Rakyat), TRI (Tentara Republik Indonesia) dan TNI (Tentara Nasional Indonesia). Kedua, jika PETA dianggap sebagai cikal bakal TNI, maka KNIL dan beberapa satuan keprajuritan diabaikan. Padahal, beberapa bekas perwira KNIL memiliki peran penting di tubuh BKR hingga TNI.Kata kunci: BKR, Tentara, TNIAbstractThe main subject this study is BKR – Indonesian civil defense corps – as origin of Indonesian Military. This study is new interpretation about the origin of TNI (Indonesian National Armed Forces) now. Many opinion refer to PETA as civil defense corps in Japanese occupation era. Study emlpoys a Historical Method, which consists of four stage: Heuristic, Critic, Interpretation, Historiography. The study utilize some sources such as newspaper, magazine, and book. Main finding of this study is PETA had dispersed as legality and formally and BKR was formed as the firts corps after Independence of Indonesia. Futhermore, BKR changed to TKR (Tentara Keamanan Rakyat), TKR (Tentara Keselamatan Rakyat), TRI (Tentara Republik Indonesia) until TNI (Tentara Nasional Indonesia). If PETA is considered as origins of Indonesian Military, then it ignore KNIL – a colonial armed forces – and the other defence corps. Even though the eks KNIL’s officer have important role in military managenment of BKR until TNI.Keywords: BKR, Military, TNI

A New Interpretation of the Structure and Solvent Dependence of the Far UV Circular Dichroism Spectrum of Short Oligopeptides

2019 ◽  
Author(s):  
Anshuman Kumar ◽  
Reinhard Schweitzer-Stenner ◽  
Bryan Wong
Keyword(s):  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Cd Spectra ◽  
Functional Theory ◽  
Polyproline Ii ◽  
Solvent Dependence ◽  
Explicit Consideration ◽  
New Interpretation ◽  
Implicit And Explicit ◽  
Explicit Water

In this work, we carry out new time-dependent density functional theory calculations on the cationic tripeptide GAG in implicit and explicit water to determine the transitions that give rise to the observed CD signals of polyproline II and β-strand conformations. Our results reveal a plethora of electronic transitions that are governed by configurational interactions between multiple molecular orbital transitions of comparable energy. We also show that reproducing the CD spectra of polyproline II and β-strand conformations requires the explicit consideration of water molecules. The structure dependence of delocalized occupied orbitals contributes to the experimentally-observed invalidation of Flory’s isolated pair hypothesis.

A New Interpretation of the Structure and Solvent Dependence of the Far UV Circular Dichroism Spectrum of Short Oligopeptides

2019 ◽  
Author(s):  
Anshuman Kumar ◽  
Reinhard Schweitzer-Stenner ◽  
Bryan Wong
Keyword(s):  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Cd Spectra ◽  
Functional Theory ◽  
Polyproline Ii ◽  
Solvent Dependence ◽  
Explicit Consideration ◽  
New Interpretation ◽  
Implicit And Explicit ◽  
Explicit Water

In this work, we carry out new time-dependent density functional theory calculations on the cationic tripeptide GAG in implicit and explicit water to determine the transitions that give rise to the observed CD signals of polyproline II and β-strand conformations. Our results reveal a plethora of electronic transitions that are governed by configurational interactions between multiple molecular orbital transitions of comparable energy. We also show that reproducing the CD spectra of polyproline II and β-strand conformations requires the explicit consideration of water molecules. The structure dependence of delocalized occupied orbitals contributes to the experimentally-observed invalidation of Flory’s isolated pair hypothesis.

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