121,772 research outputs found
On the affine Hecke category for SL3
No full textWe study the diagrammatic Hecke category associated with the affine Weyl group of type A~ 2 . More precisely we find a (surprisingly simple) basis in characteristic zero for the Hom spaces between indecomposable objects, that we call indecomposable double leaves
Pre-canonical bases on affine Hecke algebras
No full textFor any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases {N-i}1 <= i <= m+1 (where m is the height of the highest root) of the spherical Hecke algebra that interpolates between the standard basis N-1 and the canonical basis Nm+1. The expansion of Ni+1 in terms of the Ni is in many cases very simple and we conjecture that in type A it is positive
p-Jones-Wenzl idempotents
No full textFor a prime number p and any natural number n we introduce, by giving an explicit recursive formula, the p-Jones-Wenzl projector JWnp, an element of the Temperley-Lieb algebra TLn(2) with coefficients in Fp. We prove that these projectors give the indecomposable objects in the A ̃1-Hecke category over Fp, or equivalently, they give the projector in EndSLjavax.xml.bind.JAXBElement@6cdb2f49(Fjavax.xml.bind.JAXBElement@2c3fdb2 ̅)((Fp2)⊗n) to the top tilting module. The way in which we find these projectors is by categorifying the fractal appearing in the expression of the p-canonical basis in terms of the Kazhdan-Lusztig basis for A ̃1
Counterexamples to the forking path conjeture
No full textIn 2011, N. Libedinsky studied in [1] morphisms induced by paths in the
reduced expression graph of extra-large Coxeter systems. He showed that mor phisms induced by complete paths are idempotents that act as projectors. In
2016, B. Elias provides in [2] an extension of his work with M. Khovanov [3],
where they gave a diagrammatic presentation of the category of Bott-Samelson
bimodules BSBim. Here, morphisms can be translated into linear combinations
of planar graphs, and stacking planar graphs can be interpreted as composing
morphisms. Elias uses his diagrammatic calculus to construct an idempotent in
the reduced expressions graph for the longest element w0 in the symmetric group
Sn, Rex(w0,n). This idempotent can also be described by complete paths. These
observations, plus a considerable number of computer comprobations, motivate
Libedinsky to formulate the Forking Path Conjecture [4, Section 6.3].
Conjecture 1 (Forking Path Conjecture) Let x ∈ Sn, let p, q be two complete
paths with the same starting points and the same ending points in the reduced
expression graph of x. The morphisms induced by these paths are equal.
While trying to prove Libedinsky’s conjecture, a counterexample was found.
In this document we prove the conjecture for all but one element in S4. The
outstanding element is the one that sends 1 to 4, 2 to 2, 3 to 3, and 4 to 1Beca Nacional de Doctorado ANID
Nº 21171339Versión original del auto
The Geometric Formula for affine Weyl groups
No full textLet W be an affine Weyl group with corresponding finite Weyl group Wf . For each
λ, a dominant coweight, corresponds an element θ(λ) ∈ W. With N. Libedinsky and D.
Plaza, we produce a conjecture called the Geometric Formula predicting the following:
the cardinality of the set of elements in W that are lesser or equal to θ(λ) in the Bruhat
order, is a linear combination (with coefficients not depending on λ) of the volumes of
the faces of the polytope Conv(λ), constructed as the convex hull of the set Wf · λ.
We prove the geometric formula for type fA3, by giving general algebraic and geometric
constructions for the set ≤ θ(λ). We study the polytope Conv(λ), its faces, and give
some formulas to compute their volumes of the corresponding dimension.Versión original del auto
The Image of the Southern Urals in the Memoirs of Y. N. Libedinsky “Education of the Soul” as the Basis of the Exposition of the Literary Museum
No full textСтатья посвящена осмыслению метода сторителлинга в контексте нахождения новаторского материала для заполнения пространства литературного музея. Опираясь на автобиографическое произведение Ю. Н. Либединского «Воспитание души», исследуется понимание данного подхода, которое состоит в эмоциональности, соотношении, взаимном дополнении биографического, художественного и историко-культурного контекста территории Южного Урала. В материале представленного исследования показывается основание, на котором может выстраиваться новая форма потенциальной экспозиции для литературного музея.The article is devoted to understanding the method of “storytelling” in the context of finding innovative material to fill the space of a literary museum. Based on the autobiographical work of Y. N. Libedinsky “Education of the Soul”, the understanding of this approach is investigated, which consists in emotionality, correlation, complementarity of the biographical, artistic and historical-cultural context of the territory of the Southern Urals. The material of the presented research shows the basis on which a new form of potential exposition for a literary museum can be built. Keywords: storytelling, context, city culture, image of the Urals, autobiography
A Multi-Language Comparison of Influences on Author Verification using Character N-Grams
No full textWe create a new multi-language corpus for author verification based on Wikipedia talkpages, and evaluate the influence that differences in topic and time have on character n-gram author profiles. Topic alignment between two texts is found to increase author verification precision, and an authors writing style is found to change over time, but not more significantly after 3 years than after 1 year.Information ArchitectureWISElectrical Engineering, Mathematics and Computer Scienc
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
The vanishing author in computer-generated works: a critical analysis of recent Australian case law
No full textAbstract
The use of software is ubiquitous in the creation of many copyright works, yet the requirement in copyright law that every work have a human author who engages in independent intellectual effort means that its use may prevent copyright subsistence. Several recent Australian cases have refocused attention on authorship as an essential criterion of copyright subsistence, and these cases suggest that much computer-produced output may be authorless and thus lack copyright protection. This article, the first in a two-part series, analyses how each case deals with the question of authorship of computer-produced works and why the use of software diminishes copyright protection for a significant number of computer-generated works. The article critiques the application of conventional notions of human authorship developed in the pre-computer age to modern productions and suggests alternative approaches to authorship that satisfy both the major objectives of copyright policy and the need to adapt to the computer age. The article argues that, without a broader judicial approach to authorship of computer-generated works, Parliament must remedy the lacuna in protection for these ‘authorless’ works. Possible solutions for reform are suggested. In a forthcoming article, the author comprehensively examines those reform proposals
Diffusive author(s), cohesive author: Analysis of S/N (1994)
No full textThis study indicates the ways in which various aspects of the author(s) are brought forth in Dumb type’s performance art, the S/N production. Previous research has suggested a non-hierarchical organization of Dumb type and the absence of a “privileged author” in Dumb type’s collaborative work, S/N. However, the results that I have investigated from member’s interviews on the creative process of S/N along with my analysis of the recorded images of S/N, indicate a different aspect of the author(s). First, S/N was created through, so to speak, the collective ideas of the members of Dumb type. Further, S/N has at least nine quotations from previous performances, installations, and printed writings, besides the work-in-progress technique. Explicating one of the “author functions” as given by Michel Foucault, each text has plural subjects of the author. However, it has been revealed from members’ interviews that Teiji Furuhashi had a decision-making role in selecting the members’ ideas within the performance. Since then, S/N has had plural subjects of creation; however, Furuhashi is one of the subjects of creation along with the “privileged author.” S/N has plural authors (diffusive authors) yet at the same time, it has a “privileged author,” Teiji Furuhashi (cohesive author)
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