scholarly journals Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Alexander Woo
Keyword(s):  
International Audience ◽  
Lusztig Polynomials

International audience Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial$ P_id,w(q)=1+q^h$ for some $h$. On démontre la conjecture de Billey et Braden sur les permutations w pour lesquelles le polynôme de Kazhdan-Lusztig $P_id,w(q)=1+q^h$ pour un entier $h$. On emploie une résolution des singularités présentées par Cortez et une méthode de Polo pour calculer ces polynômes.

scholarly journals Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Francesco Brenti ◽  
Fabrizio Caselli
Keyword(s):  
Combinatorial Formula ◽  
Quasisymmetric Functions ◽  
International Audience ◽  
Bruhat Graph ◽  
Lusztig Polynomials

International audience We obtain a nonrecursive combinatorial formula for the Kazhdan-Lusztig polynomials which holds in complete generality and which is simpler and more explicit than any existing one, and which cannot be linearly simplified. Our proof uses a new basis of the peak subalgebra of the algebra of quasisymmetric functions. On montre une formule combinatoire pour les polynômes de Kazhdan-Lusztig qui est valable en toute généralité. Cette formule est plus simple et plus explicite que toutes les autres formules connues; de plus, elle ne peut pas être simplifiée linéairement. La preuve utilise une nouvelle base pour la sous-algèbre des sommets de l’algèbre des fonctions quasi-symmetriques.

scholarly journals An immanant formulation of the dual canonical basis of the quantum polynomial ring

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Mark Skandera ◽  
Justin Lambright
Keyword(s):  
Polynomial Ring ◽  
Canonical Basis ◽  
Polynomial Rings ◽  
Dual Canonical Basis ◽  
International Audience ◽  
Quantum Polynomial ◽  
Lusztig Polynomials

International audience We show that dual canonical basis elements of the quantum polynomial ring in $n^2$ variables can be expressed as specializations of dual canonical basis elements of $0$-weight spaces of other quantum polynomial rings. Our results rely upon the natural appearance in the quantum polynomial ring of Kazhdan-Lusztig polynomials, $R$-polynomials, and certain single and double parabolic generalizations of these. Nous démontrons que des éléments de la base canonique duale de l'anneau quantique des polynômes en $n^2$ variables peuvent s'exprimer en termes des spécialisations d'éléments de la base canonique duale des espaces de poids $0$ d'autres anneaux quantiques. Nos résultats dépendent fortement de l'apparition naturelle des polynômes de Kazhdan-Lusztig, des $R$-polynômes, et de certaines généralisations simplement et doublement paraboliques de ces polynômes dans l'anneau quantique.

scholarly journals Moment graphs and KL-polynomials

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Martina Lanini
Keyword(s):  
New Techniques ◽  
International Audience ◽  
Combinatorial Data ◽  
Lusztig Polynomials

International audience Motivated by a result of Fiebig (2007), we categorify some properties of Kazhdan-Lusztig polynomials via sheaves on Bruhat moment graphs. In order to do this, we develop new techniques and apply them to the combinatorial data encoded in these moment graphs. Motivés par un résultat de Fiebig (2007), nous catégorisons certaines propriétés des polynômes de Kazhdan-Lusztig en utilisant faisceaux sur les graphes moment de Bruhat. Pour faire ça, nous développons de nouvelles techniques et les appliquons ensuite aux données combinatoires encodées dans ces graphes moment.

scholarly journals Deodhar Elements in Kazhdan-Lusztig Theory

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Brant Jones
Keyword(s):  
Coxeter Groups ◽  
Pattern Avoidance ◽  
Weyl Groups ◽  
Schubert Varieties ◽  
Combinatorial Formula ◽  
Nous Obtenons ◽  
Integer Coefficients ◽  
Nous Montrons ◽  
International Audience ◽  
Lusztig Polynomials

International audience The Kazhdan-Lusztig polynomials for finite Weyl groups arise in representation theory as well as the geometry of Schubert varieties. It was proved very soon after their introduction that they have nonnegative integer coefficients, but no simple all positive interpretation for them is known in general. Deodhar has given a framework, which generally involves recursion, to express the Kazhdan-Lusztig polynomials in a very attractive form. We use a new kind of pattern-avoidance that can be defined for general Coxeter groups to characterize when Deodhar's algorithm yields a non-recursive combinatorial formula for Kazhdan-Lusztig polynomials $P_{x,w}(q)$ of finite Weyl groups. This generalizes results of Billey-Warrington which identified the $321$-hexagon-avoiding permutations, and Fan-Green which identified the fully-tight Coxeter groups. We also show that the leading coefficient known as $\mu (x,w)$ for these Kazhdan―Lusztig polynomials is always either $0$ or $1$. Finally, we generalize the simple combinatorial formula for the Kazhdan―Lusztig polynomials of the $321$-hexagon-avoiding permutations to the case when $w$ is hexagon avoiding and maximally clustered. Les polynômes de Kazhdan-Lusztig $P_{x,w}(q)$ des groupes de Weyl finis apparaissent en théorie des représentations, ainsi qu’en géométrie des variétés de Schubert. Il a été démontré peu après leur introduction qu’ils avaient des coefficients entiers positifs, mais on ne connaît toujours pas d’interprétation combinatoire simple de cette propriété dans le cas général. Deodhar a proposé un cadre donnant un algorithme, en général récursif, calculant des formules attractives pour les polynômes de Kazhdan-Lusztig. Billey-Warrington ont démontré que cet algorithme est non récursif lorsque$w$ évite les hexagones et les $321$ et qu’il donne des formules combinatoires simples. Nous introduisons une notion d’évitement de schémas dansles groupes de Coxeter quelconques nous permettant de généraliser les résultats de Billey-Warrington à tout groupe de Weyl fini. Nous montrons que le coefficient de tête $\mu (x,w)$ de ces polynômes de Kazhdan-Lusztig est toujours $0$ ou $1$. Cela généralise aussi des résultats de Fan-Greenqui identifient les groupes de Coxeter complètement serrés. Enfin, en type $A$, nous obtenons une classe plus large de permutations évitant la récursion.

Somethin’ about Scandinavia: Danish Shorts on the Post-war International Scene

2018 ◽  
Author(s):  
C. Claire Thomson
Keyword(s):  
United Nations ◽  
International Collaboration ◽  
Marshall Plan ◽  
The Third ◽  
Animated Film ◽  
International Audience ◽  
Post War ◽  
Nordic Cooperation

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.

Conclusion

2018 ◽  
Author(s):  
Alistair Fox
Keyword(s):  
National Identity ◽  
New Zealand ◽  
Identity Formation ◽  
Essential Role ◽  
Coming Of Age ◽  
Financial Returns ◽  
Self Recognition ◽  
International Audience ◽  
National Identity Formation

The conclusion reaffirms the essential role played by cinema generally, and the coming-of-age genre in particular, in the process of national identity formation, because of its effectiveness in facilitating self-recognition and self-experience through a process of triangulation made possible, for the most part, by a dialogue with some of the nation’s most iconic works of literature. This section concludes by point out the danger posed, however, by an observable trend toward generic standardization in New Zealand films motivated by a desire to appeal to an international audience out of consideration for the financial returns expected by funding bodies under current regimes.

Early Cinema in Scotland

2018 ◽  
Keyword(s):  
Social History ◽  
Small Towns ◽  
Early Cinema ◽  
Popular Song ◽  
Feature Film ◽  
Local Newspapers ◽  
The Social ◽  
Production History ◽  
History Of ◽  
International Audience

This collection of essays, drawn from a three-year AHRC research project, provides a detailed context for the history of early cinema in Scotland from its inception in 1896 till the arrival of sound in the early 1930s. It details the movement from travelling fairground shows to the establishment of permanent cinemas, and from variety and live entertainment to the dominance of the feature film. It addresses the promotion of cinema as a socially ‘useful’ entertainment, and, distinctively, it considers the early development of cinema in small towns as well as in larger cities. Using local newspapers and other archive sources, it details the evolution and the diversity of the social experience of cinema, both for picture goers and for cinema staff. In production, it examines the early attempts to establish a feature film production sector, with a detailed production history of Rob Roy (United Films, 1911), and it records the importance, both for exhibition and for social history, of ‘local topicals’. It considers the popularity of Scotland as an imaginary location for European and American films, drawing their popularity from the international audience for writers such as Walter Scott and J.M. Barrie and the ubiquity of Scottish popular song. The book concludes with a consideration of the arrival of sound in Scittish cinemas. As an afterpiece, it offers an annotated filmography of Scottish-themed feature films from 1896 to 1927, drawing evidence from synopses and reviews in contemporary trade journals.

Spiritual and Ecclesiastical Biographies: Research, Results, and Reading, ed. Anders Jarlert. Konferenser, 94. Stockholm: Kungl. Vitterhets Historie och Antikvitets Akademien, 2017, 245 pp.

Mediaevistik ◽  
2018 ◽  
Vol 31 (1) ◽  
pp. 327-327
Author(s):  
Albrecht Classen
Keyword(s):  
South Africa ◽  
Middle Ages ◽  
Life Writing ◽  
Emeritus Professor ◽  
Royal Swedish Academy ◽  
Research Results ◽  
International Audience ◽  
Binghamton University ◽  
Sciences Sociales ◽  
The Middle Ages

The papers combined in this volume were originally presented at a conference at the Royal Swedish Academy of Letters, History and Antiquities in Stockholm, June 11–12, 2015. The explicit purpose of this event and the subsequent volume was to expose the work of Swedish and other scholars on the genre of biographies to an international audience, reflecting on life-writing or ego-documents, emphasizing spiritual autobiographies. According to the brief bios at the end of the book, Robert Swanson, for instance, is Emeritus Professor at Binghamton University; Jean-Mark Ticchi teaches at the Centre d’Etudes en Sciences Sociales du Religieux in Paris; and Enock Bongani Zulu was lecturer at the Lutheran Theological Institute in Pietermaritzburg, South Africa. The book cover is decorated with an image showing a page in Margery Kempe’s Book from ca. 1440, indicating that the focus might rest on the Middle Ages. This is only very partially the case.

Food museums as cultural institutions and tourist attractions: Evidence from Italy

2020 ◽  
Author(s):  
Roberta Garibaldi ◽  
Andrea Pozzi
Keyword(s):  
Private Companies ◽  
Tourist Attractions ◽  
Local Stakeholders ◽  
Cooking Shows ◽  
International Audience ◽  
External Relationships ◽  
Museum Experience ◽  
Public Museums ◽  
Modes Of Engagement ◽  
Heritage Interpretation

In recent years, food museums have turned into popular attractions for tourists. Scholars and practitioners have emphasized their role as agents of preservation, education and cultural heritage interpretation, but devoted little attention to tourism related issues. To fill the gap, this paper investigates Italian food museums in order to assess their characteristics, tasks, audience and modes of engagement. Findings suggest that community engagement is an important task along with safeguarding and promoting food heritage. Creating or improving external relationships is crucial for public museums to get recognized for their role and value. For museums operated by private companies, engaging with local stakeholders and residents serves not just a branding purpose, but also in awakening their interest in past and present issues concerning the product (nutrition, safety, taste, cultural and social values). The majority of Italian food museums mainly appeal to domestic travelers, which indicates the potential to reach a larger, international audience. Visibility and language issues remain crucial to reach international tourists but reframing the museum experience is also essential to meet new visitors’ needs. Exploiting traditional exhibitions of food-related objects with multimedia technology and practical activities such as classes, workshops, cooking shows can help in engaging the audiences.

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