scholarly journals Combinatorial descriptions of the crystal structure on certain PBW bases

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Ben Salisbury ◽  
Adam Schultze ◽  
Peter Tingley
Keyword(s):  
Crystal Structure ◽  
Weyl Group ◽  
Lie Algebra ◽  
Simple Complex ◽  
International Audience ◽  
The Relationship

International audience Lusztig's theory of PBW bases gives a way to realize the crystal B(∞) for any simple complex Lie algebra where the underlying set consists of Kostant partitions. In fact, there are many different such realizations, one for each reduced expression for the longest element of the Weyl group. There is an algorithm to calculate the actions of the crystal operators, but it can be quite complicated. For ADE types, we give conditions on the reduced expression which ensure that the corresponding crystal operators are given by simple combinatorial bracketing rules. We then give at least one reduced expression satisfying our conditions in every type except E8, and discuss the resulting combinatorics. Finally, we describe the relationship with more standard tableaux combinatorics in types A and D.

scholarly journals Gelfand―Tsetlin Polytopes and Feigin―Fourier―Littelmann―Vinberg Polytopes as Marked Poset Polytopes

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Federico Ardila ◽  
Thomas Bliem ◽  
Dido Salazar
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Ehrhart Polynomial ◽  
International Audience ◽  
Order Polytope ◽  
Finite Partially Ordered Set ◽  
The Relationship

International audience Stanley (1986) showed how a finite partially ordered set gives rise to two polytopes, called the order polytope and chain polytope, which have the same Ehrhart polynomial despite being quite different combinatorially. We generalize his result to a wider family of polytopes constructed from a poset P with integers assigned to some of its elements. Through this construction, we explain combinatorially the relationship between the Gelfand–Tsetlin polytopes (1950) and the Feigin–Fourier–Littelmann–Vinberg polytopes (2010, 2005), which arise in the representation theory of the special linear Lie algebra. We then use the generalized Gelfand–Tsetlin polytopes of Berenstein and Zelevinsky (1989) to propose conjectural analogues of the Feigin–Fourier–Littelmann–Vinberg polytopes corresponding to the symplectic and odd orthogonal Lie algebras. Stanley (1986) a montré que chaque ensemble fini partiellement ordonné permet de définir deux polyèdres, le polyèdre de l'ordre et le polyèdre des cha\^ınes. Ces polyèdres ont le même polynôme de Ehrhart, bien qu'ils soient tout à fait distincts du point de vue combinatoire. On généralise ce résultat à une famille plus générale de polyèdres, construits à partir d'un ensemble partiellement ordonné ayant des entiers attachés à certains de ses éléments. Par cette construction, on explique en termes combinatoires la relation entre les polyèdres de Gelfand-Tsetlin (1950) et ceux de Feigin-Fourier-Littelmann-Vinberg (2010, 2005), qui apparaissent dans la théorie des représentations des algèbres de Lie linéaires spéciales. On utilise les polyèdres de Gelfand-Tsetlin généralisés par Berenstein et Zelevinsky (1989) afin d'obtenir des analogues (conjecturés) des polytopes de Feigin-Fourier-Littelmann-Vinberg pour les algèbres de Lie symplectiques et orthogonales impaires.

SYMMETRY INSIGHTS FOR DESIGN OF SUPERCOMPUTER NETWORK TOPOLOGIES: ROOTS AND WEIGHTS LATTICES

2012 ◽  
Vol 26 (31) ◽  
pp. 1250169 ◽  
Author(s):  
YUEFAN DENG ◽  
ALEXANDRE F. RAMOS ◽  
JOSÉ EDUARDO M. HORNOS
Keyword(s):  
Weyl Group ◽  
Lie Algebra ◽  
Root Systems ◽  
Hardware Architecture ◽  
Classification Theorem ◽  
Simple Complex ◽  
Half Integer ◽  
Network Topologies ◽  
Integer Weight

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

Contractual Relationships among Artists, Record Labels, and Artist Management Companies in Japan

2020 ◽  
Author(s):  
Kazuhiro Ando
Keyword(s):  
Music Industry ◽  
Music Business ◽  
Know How ◽  
Contractual Relationships ◽  
The World ◽  
Employee Relationship ◽  
International Audience ◽  
Music Market ◽  
Japanese Music ◽  
The Relationship

Although Japan is the second largest music market in the world, the structure and practices of the music industry are little understood internationally. People overseas need to know how the music business works in Japan so that they can conduct business comfortably. The Japanese music industry has unique features in some respects. First, Japanese record labels remain heavily dependent on traditional physically packaged music although its profitability is much lower than that of digital distribution. Second, full-scale competition in the music copyright management business has just begun. While JASRAC monopolized this market for more than sixty years, the new entrant, NexTone has gradually increased the market share thanks to the frustration experienced by many music publishers and songwriters in their dealings with JASRAC. Third, the relationship between artists and artist management companies is more like an employer-employee relationship than a client-agent relationship. Artist management companies are fully invested in discovering, nurturing, and marketing young artists just the way big businesses handle their recruits. This chapter illuminates practices of the Japanese music industry for an international audience.

scholarly journals Generation of an Isogenic Collection of Yeast Actin Mutants and Identification of Three Interrelated Phenotypes

Genetics ◽  
2001 ◽  
Vol 157 (2) ◽  
pp. 533-543
Author(s):  
Johanna L Whitacre ◽  
Dana A Davis ◽  
Kurt A Toenjes ◽  
Sharon M Brower ◽  
Alison E M Adams
Keyword(s):  
Crystal Structure ◽  
Growth Rates ◽  
Small Region ◽  
Wild Type ◽  
Large Collection ◽  
Growth Defects ◽  
Cytoskeletal Function ◽  
Highly Correlated ◽  
The Relationship ◽  
Mutant Cells

Abstract A large collection of yeast actin mutations has been previously isolated and used in numerous studies of actin cytoskeletal function. However, the various mutations have been in congenic, rather than isogenic, backgrounds, making it difficult to compare the subtle phenotypes that are characteristic of these mutants. We have therefore placed 27 mutations in an isogenic background. We used a subset of these mutants to compare the degree to which different actin alleles are defective in sporulation, endocytosis, and growth on NaCl-containing media. We found that the three phenotypes are highly correlated. The correlations are specific and not merely a reflection of general growth defects, because the phenotypes are not correlated with growth rates under normal conditions. Significantly, those actin mutants exhibiting the most severe phenotypes in all three processes have altered residues that cluster to a small region of the actin crystal structure previously defined as the fimbrin (Sac6p)-binding site. We examined the relationship between endocytosis and growth on salt and found that shifting wild-type or actin mutant cells to high salt reduces the rate of α-factor internalization. These results suggest that actin mutants may be unable to grow on salt because of additive endocytic defects (due to mutation and salt).

scholarly journals The strongly defective double perovskite Sr11Mo4O23: crystal structure in relation to ionic conductivity

2014 ◽  
Vol 47 (4) ◽  
pp. 1395-1401 ◽  
Author(s):  
Carlos A. López ◽  
José C. Pedregosa ◽  
Diego G. Lamas ◽  
José A. Alonso
Keyword(s):  
Crystal Structure ◽  
Ionic Conductivity ◽  
Powder Diffraction ◽  
Double Perovskite ◽  
Ionic Mobility ◽  
Neutron Powder Diffraction Data ◽  
Complex Crystal Structure ◽  
Citrate Precursors ◽  
The Relationship ◽  
Complex Crystal

The crystal structure and ionic conductivity properties of a novel microcrystalline Sr11Mo4O23ceramic material are presented. This material has been prepared by thermal treatment up to 1473 K, in air, of previously decomposed citrate precursors. The complex crystal structure was refined from combined X-ray powder diffraction and neutron powder diffraction data. The formula of this phase can be rewritten as Sr1.75□0.25SrMoO5.75, highlighting the relationship with double perovskitesA2B′B′′O6. At room temperature, the crystal structure is tetragonal in space groupI41/a, witha= 11.6107 (6) Å,c= 16.422 (1) Å andV = 2213.8 (2) Å3. The crystal network contains O anion and Sr cation vacancies. The structure is complex, with Sr, Mo and O atoms distributed over four, two and six distinct Wyckoff sites, respectively. Only one of the Sr sites (SrO6) corresponds to the octahedral network; one of the two MoO6types of octahedra is axially distorted. The three other Sr positions occupy theAsite with higher coordination. There is an occupational deficit of O atoms of 22 (4)%. This defective framework material presents an interesting ionic mobility, enhanced above 773 K owing to a further reduction in the oxygen content.

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