124,869 research outputs found
Introduction to Soergel bimodules
No full textThis book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research. This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers
A topological approach to Soergel theory
No full textInternational audienceWe develop a "Soergel theory" for Bruhat-constructible perverse sheaves on the flag variety G/B of a complex reductive group G, with coefficients in an arbitrary field k. Namely, we describe the endomorphisms of the projective cover of the skyscraper sheaf in terms of a "multiplicative" coinvariant algebra, and then establish an equivalence of categories between projective (or tilting) objects in this category and a certain category of "Soergel modules" over this algebra. We also obtain a description of the derived category of T-monodromic k-sheaves on G/U (where U,T ⊂ B are the unipotent radical and the maximal torus), as a monoidal category
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Simple transitive 2-representations of Soergel bimodules in type B<sub>2</sub>
No full textWe prove that every simple transitive 2-representation of the fiat 2-category of Soergel bimodules (over the coinvariant algebra) in type B2 is equivalent to a cell 2-representation. We also describe some general properties of the 2-category of Soergel bimodules for arbitrary finite dihedral groups.</p
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Sur la catégorie des bimodules de Soergel
No full textRésuméLa catégorie B de Soergel d'un système de Coxeter (W,S) est une catégorie de bimodules sur une algèbre de polynômes sur laquelle W agit. C'est une catégorification de l'algèbre de Hecke de (W,S). Dans cet article nous donnons une description combinatoire des espaces de morphismes dans B. En corollaire, on obtient une description analogue des morphismes dans O0-proj, où O0 est le bloc principal de la catégorie O de BGG
UV laser-assisted fabrication of ridge waveguides in lithium niobate crystals
No full textWe present a UV laser-assisted method for the fabrication of ridge waveguides in lithium niobate. The UV laser irradiation step provides the refractive index change required for the vertical light confinement in the waveguide and also defines the ferroelectric domain pattern which produces the ridge structures after chemical etching
Simple transitive 2-representations for some 2-subcategories of Soergel bimodules
No full textWe classify simple transitive 2-representations of certain 2-subcategories of the 2-category of Soergel bimodules over the coinvariant algebra in Coxeter types B-2 and I-2(5). In the I-2(5) case it turns out that simple transitive 2-representations are exhausted by cell 2-representations. In the B-2 case we show that, apart from cell 2-representations, there is a unique, up to equivalence, additional simple transitive 2-representation and we give an explicit construction of this 2-representation. (C) 2016 Elsevier B.V. All rights reserved.Swedish Research Counci
Pragmatic Case Studies as a Source of Unity in Applied Psychology
No full textTo unify or not to unify applied psychology: that is the question. In this article we review pendulum swings in the historical efforts to answer this question—from a comprehensive, positivist, “top-down,” deductive yes between the 1930s and the early 60s, to a postmodern no since then. A rationale and proposal for a limited, “bottom-up,” inductive yes in applied psychology is then presented, employing a case-based paradigm that integrates both positivist and postmodern themes and components. This paradigm is labeled “pragmatic psychology” and, its specific use of case studies, the “Pragmatic Case Study Method” (“PCS Method”). We call for the creation of peer-reviewed journal-databases of pragmatic case studies as a foundational source of unifying applied knowledge in our discipline. As one example, the potential of the PCS Method for unifying different angles of theoretical regard is illustrated in an area of applied psychology, psychotherapy, via the case of Mrs. B. The article then turns to the broader historical and epistemological arguments for the unifying nature of the PCS Method in both applied and basic psychology.Peer reviewe
Dualität in der Kategorie von Andersen-Jantzen-Soergel
No full textIn the early 1990s, a combinatorial model was introduced by Andersen, Jantzen and Soergel to describe certain representations of the following two situations:
a) U_p is the quantised enveloping algebra of a complex Lie algebra at a p-th root of unity, where p > 1 is an odd integer (and prime to 3 if the corresponding root system is of type G_2),
b) Lie(G_k), where G_k is a connected, simply connected semisimple algebraic group over an algebraically closed field k of char p > h, where h is the Coxeter number of the corresponding root system.
The relation between these two situations is essential to show Lusztig’s Modular Conjecture for char p >> 0. This conjecture provides a character formula for representations of connected reductive algebraic groups over an algebraically closed field k with char k = p > h. With the work by Andersen, Jantzen and Soergel it can be deduced from its char 0 analogue, Lusztig’s Quantum Conjecture.
This model is realised by a combinatorial category K_k and its full subcategory of so-called special objects M_k. The definition of special objects is very technical. A better understanding or an intrinsic description by categorical properties of M_k could lead for example to an improvement of the upper bounds on exceptional primes.
This thesis contains a detailed examination of M_k. One of the major results is to describe the behaviour of duality where an important class of special objects consists of self-dual objects. Another major result is the description of the centre of M_k.Anfang der 1990er Jahre führten Andersen, Jantzen und Soergel ein kombinatorisches Modell ein, um gewisse Darstellungen der folgenden zwei Situationen zu beschreiben:
a) U_p ist die quantisierte einhüllende Algebra einer komplexen Lie-Algebra an einer p-ten Einheitswurzel, wobei p > 1 eine ungerade ganze Zahl ist (und prim zu 3 wenn das zugrundeliegende Wurzelsystem vom Typ G_2 ist),
b) Lie(G_k), wobei G_k eine zusammenhängende, einfach zusammenhängende halbeinfache algebraische Gruppe über einem algebraisch abgeschlossenen Körper k mit char k > h, wobei h die Coxeterzahl des zugrundeliegenden Wurzelsystems ist.
Der Zusammenhang zwischen diesen beiden Situationen ist grundlegend, um die Modulare Lusztig-Vermutung für char p>> 0 zu zeigen. Diese Vermutung stellt eine Charakterformel für Darstellungen zusammenhängender reduktiver algebraischer Gruppen über einem algebraisch abgeschlossenen Körper k mit char k = p > h auf. Mit dem Werk von Andersen, Jantzen und Soergel kann man sie aus ihrem char 0-Analogon herleiten, der Quantum-Vermutung von Lusztig.
Dieses Modell wird durch eine kombinatorische Kategorie K_k und einer vollen Unterkategorie der sogenannten speziellen Objekte M_k realisiert. Die Definition der speziellen Objekte ist sehr technisch. Ein besseres Verständnis oder eine intrinsische Beschreibung durch kategorielle Eigenschaften von M_k könnten beispielsweise zu einer Verbesserung einer oberen Schranke für Ausnahmeprimzahlen der Modularen Lusztig-Vermutung führen.
Diese Arbeit enthält eine detaillierte Untersuchung von M k . Ein Hauptresultat ist die Beschreibung des Verhaltens der Dualität, wobei eine wichtige Klasse der speziellen Objekte aus selbstdualen Objekten besteht. Ein weiteres wichtiges Resultat ist die Beschreibung des Zentrums von M_k
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