1,720,960 research outputs found
Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category
Full text linkIn this paper, we study relationships between the normalized characters of
symmetric groups and the Boolean cumulants of Young diagrams. Specifically, we
show that each normalized character is a polynomial of twisted Boolean
cumulants with coefficients being non-negative integers, and conversely, that,
when we expand a Boolean cumulant in terms of normalized characters, the
coefficients are again non-negative integers. The main tool is Khovanov's
Heisenberg category and the recently established connection of its center to
the ring of functions on Young diagrams, which enables one to apply graphical
manipulations to the computation of functions on Young diagrams. Therefore,
this paper is an attempt to deepen the connection between the asymptotic
representation theory and graphical categorification.Comment: 29 page
Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
No full textThe analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a positive contraction acting on a ''doubled'' one-particle space with an additional structure defines a unique PfPP. Recently, Olshanski inverted the direction from free fermions to DPPs, proposed a scheme to construct a fermionic state from a quasi-invariant probability measure, and introduced the notion of perfectness of a probability measure. We propose a method to check the perfectness and show that Schur measures are perfect as long as they are quasi-invariant under the action of the symmetric group. We also study conditional measures for PfPPs associated with projection operators. Consequently, we show that the conditional measures are again PfPPs associated with projection operators onto subspaces explicitly described.The author is grateful to Makoto Katori, Tomoyuki Shirai, and Sho Matsumoto for discussions and comments on the manuscript. He also thanks the anonymous referees for their useful suggestions for improvements of the manuscript. This work was supported by the Grant-in-Aid for JSPS Fellows (No. 19J01279)
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe 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
Decomposition of a Finite-Dimensional Unitary Representation of SU(2) into Irreducible Representations
No full textSimple branching in the representation theory of the symmetric groups and the Gelfand–Tsetlin algebra
No full textThe Quantum Group Dual of the First-Row Subcategory for the Generic Virasoro VOA
No full textFunding Information: SK is supported by the Grant-in-Aid for JSPS Fellows (No. 19J01279). Publisher Copyright: © 2021, The Author(s).In several examples it has been observed that a module category of a vertex operator algebra (VOA) is equivalent to a category of representations of some quantum group. The present article is concerned with developing such a duality in the case of the Virasoro VOA at generic central charge; arguably the most rudimentary of all VOAs, yet structurally complicated. We do not address the category of all modules of the generic Virasoro VOA, but we consider the infinitely many modules from the first row of the Kac table. Building on an explicit quantum group method of Coulomb gas integrals, we give a new proof of the fusion rules, we prove the analyticity of compositions of intertwining operators, and we show that the conformal blocks are fully determined by the quantum group method. Crucially, we prove the associativity of the intertwining operators among the first-row modules, and find that the associativity is governed by the 6j-symbols of the quantum group. Our results constitute a concrete duality between a VOA and a quantum group, and they will serve as the key tools to establish the equivalence of the first-row subcategory of modules of the generic Virasoro VOA and the category of (type-1) finite-dimensional representations of Uq(sl2).Peer reviewe
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