scholarly journals A group representation approach to balance of gain graphs

2020 ◽  
Author(s):  
Matteo Cavaleri ◽  
Daniele D’Angeli ◽  
Alfredo Donno
Keyword(s):  
Group Representation ◽  
Gain Graphs

Recasting Bourgeois Europe

2015 ◽  
Author(s):  
Charles S. Maier ◽  
Charles S. Maier
Keyword(s):  
World War Ii ◽  
Social Vulnerability ◽  
Group Representation ◽  
Political Stability ◽  
Status Quo ◽  
European History ◽  
World War ◽  
History Of ◽  
Country Analysis ◽  
Economic Stabilization

The author, one of the most prominent contemporary scholars of European history, published this, his first book, in 1975. Based on extensive archival research, the book examines how European societies progressed from a moment of social vulnerability to one of political and economic stabilization. Arguing that a common trajectory calls for a multi country analysis, the book provides a comparative history of three European nations—France, Germany, and Italy—and argues that they did not simply return to a prewar status quo, but achieved a new balance of state authority and interest group representation. While most previous accounts presented the decade as a prelude to the Depression and dictatorships, the author suggests that the stabilization of the 1920s, vulnerable as it was, foreshadowed the more enduring political stability achieved after World War II. The immense and ambitious scope of this book, its ability to follow diverse histories in detail, and its effort to explain stabilization—and not just revolution or breakdown—have made it a classic of European history.

Glossary of Signed and Gain Graphs

10.37236/31 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
Thomas Zaslavsky
Keyword(s):  
Gain Graphs

A glossary to accompany DS8.

The Transition Matrix Between the Specht and 𝔰𝔩3 Web Bases is Unitriangular With Respect to Shadow Containment

2020 ◽  
Author(s):  
Heather M Russell ◽  
Julianna Tymoczko
Keyword(s):  
Symmetric Group ◽  
Partial Order ◽  
Transition Matrix ◽  
Group Representation ◽  
Jones Polynomial ◽  
Basis Matrix ◽  
Combinatorial Structures ◽  
Quantum Invariants ◽  
One Dimensional ◽  
Link Diagrams

Abstract Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link diagrams in terms of webs, producing quantum invariants like the well-known Jones polynomial. One important question in representation theory is to identify the relationships between different bases; coefficients in the change-of-basis matrix often describe combinatorial, algebraic, or geometric quantities (e.g., Kazhdan–Lusztig polynomials). By ”flattening” the braiding maps, webs can also be viewed as the basis elements of a symmetric group representation. In this paper, we define two new combinatorial structures for webs: band diagrams and their one-dimensional projections, shadows, which measure depths of regions inside the web. As an application, we resolve an open conjecture that the change of basis between the so-called Specht basis and web basis of this symmetric group representation is unitriangular for $\mathfrak{sl}_3$-webs ([ 33] and [ 29].) We do this using band diagrams and shadows to construct a new partial order on webs that is a refinement of the usual partial order. In fact, we prove that for $\mathfrak{sl}_2$-webs, our new partial order coincides with the tableau partial order on webs studied by the authors and others [ 12, 17, 29, 33]. We also prove that though the new partial order for $\mathfrak{sl}_3$-webs is a refinement of the previously studied tableau order, the two partial orders do not agree for $\mathfrak{sl}_3$.

Towards a computational theory of social groups: A finite set of cognitive primitives for representing any and all social groups in the context of conflict

2021 ◽  
pp. 1-62
Author(s):  
David Pietraszewski
Keyword(s):  
Social Group ◽  
Group Representation ◽  
Social Groups ◽  
Study Groups ◽  
Human Mind ◽  
Computational Theory ◽  
Mistaken Belief ◽  
Finite Set ◽  
The One ◽  
Definition Of

Abstract We don't yet have adequate theories of what the human mind is representing when it represents a social group. Worse still, many people think we do. This mistaken belief is a consequence of the state of play: Until now, researchers have relied on their own intuitions to link up the concept social group on the one hand, and the results of particular studies or models on the other. While necessary, this reliance on intuition has been purchased at considerable cost. When looked at soberly, existing theories of social groups are either (i) literal, but not remotely adequate (such as models built atop economic games), or (ii) simply metaphorical (typically a subsumption or containment metaphor). Intuition is filling in the gaps of an explicit theory. This paper presents a computational theory of what, literally, a group representation is in the context of conflict: it is the assignment of agents to specific roles within a small number of triadic interaction types. This “mental definition” of a group paves the way for a computational theory of social groups—in that it provides a theory of what exactly the information-processing problem of representing and reasoning about a group is. For psychologists, this paper offers a different way to conceptualize and study groups, and suggests that a non-tautological definition of a social group is possible. For cognitive scientists, this paper provides a computational benchmark against which natural and artificial intelligences can be held.

A description of harmonic functions via properties of the group representation of the Cayley tree

2006 ◽  
Vol 79 (3-4) ◽  
pp. 399-407 ◽  
Author(s):  
É. P. Normatov ◽  
U. A. Rozikov
Keyword(s):  
Harmonic Functions ◽  
Cayley Tree ◽  
Group Representation

scholarly journals Springer’s Weyl Group Representation via Localization

2017 ◽  
Vol 60 (3) ◽  
pp. 478-483 ◽  
Author(s):  
Jim Carrell ◽  
Kiumars Kaveh
Keyword(s):  
Weyl Group ◽  
Equivariant Cohomology ◽  
Group Representation ◽  
General Theorem ◽  
Torus Action ◽  
Cohomology Algebra ◽  
Reductive Algebraic Group ◽  
Point Set ◽  
Closed Subvariety ◽  
Springer Variety

AbstractLet G denote a reductive algebraic group over C and x a nilpotent element of its Lie algebra 𝔤. The Springer variety Bx is the closed subvariety of the flag variety B of G parameterizing the Borel subalgebras of 𝔤 containing x. It has the remarkable property that the Weyl group W of G admits a representation on the cohomology of Bx even though W rarely acts on Bx itself. Well-known constructions of this action due to Springer and others use technical machinery from algebraic geometry. The purpose of this note is to describe an elementary approach that gives this action when x is what we call parabolic-surjective. The idea is to use localization to construct an action of W on the equivariant cohomology algebra H*S (Bx), where S is a certain algebraic subtorus of G. This action descends to H*(Bx) via the forgetful map and gives the desired representation. The parabolic-surjective case includes all nilpotents of type A and, more generally, all nilpotents for which it is known that W acts on H*S (Bx) for some torus S. Our result is deduced from a general theorem describing when a group action on the cohomology of the ûxed point set of a torus action on a space lifts to the full cohomology algebra of the space.

Group Representation and Profiling

2014 ◽  
pp. 661-665
Author(s):  
Armen Aghasaryan ◽  
Makram Bouzid ◽  
Dimitre Davidov Kostadinov ◽  
Jérôme Picault
Keyword(s):  
Group Representation
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