18.712 Introduction to Representation Theory, Fall 2008 by Etingof, Pavel

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The ZX-calculus as a language for topological quantum computation by Ahmadi, FR, Kissinger, A

“…We represent such generators for the Fibonacci and Ising models, namely the encoding of qubits and the associated braid group representations, with the ZX-calculus and show that in both cases, the Yang–Baxter equation is directly connected to an important rule in the complete ZX-calculus known as the P-rule, which enables one to interchange the phase gates defined with respect to complementary bases. …”

Double copy for massive quantum particles with spin by Johansson, H, Ochirov, A

“…The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. …”

Hexagonal Convolutional Neural Networks for Hexagonal Grids by Junren Luo, Wanpeng Zhang, Jiongming Su, Fengtao Xiang

“…Then, we introduce the planer and spherical hexagonal grids and analyze the group representations for them, we review geometric deep learning, some Convolutional Neural Networks (CNNs) for hexagonal grids, and group-based equivariant convolution. …”
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Identification of a reversible quantum gate: assessing the resources by Giulio Chiribella, Giacomo Mauro D'Ariano, Martin Roetteler

“…In addition, we introduce the notion of generalized t -designs, which includes unitary t -designs and group representations as special cases. For gates forming a generalized t -design we give an explicit expression for the maximum probability of correct gate identification and we prove that there is no gap between the performances of deterministic strategies and those of probabilistic strategies. …”
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Conformal blocks from celestial gluon amplitudes. Part II. Single-valued correlators by Wei Fan, Angelos Fotopoulos, Stephan Stieberger, Tomasz R. Taylor, Bin Zhu

“…The conformal block spectrum consists of primary fields with dimensions ∆ = m + iλ, with integer m ≥ 1 and various, but always integer spin, in all group representations contained in the product of two adjoint representations.…”
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Brain activation of semantic category-based grouping in multiple identity tracking task. by Liuqing Wei, Xuemin Zhang, Chuang Lyu, Siyuan Hu, Zhen Li

“…The ACC might be responsible for the initiation and maintenance of grouping representation.…”
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Generalized matrix functions, determinant and permanent by Mohammad Hossein Jafari, Ali Reza Madadi

“…Generalized matrix functions connect some branches of mathematics such as theory of finite groups, representation theory of groups, graph theory and combinatorics, and linear and multilinear algebra.    …”
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Pacman geometries and the Hayward term in JT gravity by Raúl Arias, Marcelo Botta-Cantcheff, Pedro J. Martinez

“…Also study previous proposals on the superselection sectors, and by computing the density operator we obtain the Shannon entropy and some novel results on the symmetry group representations and edge modes. It also makes contact with the so-called defect operator found in [2]. …”
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Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century by Frédéric Barbaresco, Jean-Pierre Gazeau

“…In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). …”
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Warm Dark Matter from Higher-Dimensional Gauge Theories by Sinziana Paduroiu, Michael Rios, Alessio Marrani, David Chester

“…Warm dark matter particles with masses in the keV range have been linked with the large group representations in gauge theories through a high number of species at decoupling. …”
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Information inequalities and finite groups : an overview by Markin, Nadya, Oggier, Frédérique

“…We recall Chan's technique of constructing random variables from groups and the corresponding notion of (abelian) group representable entropic vectors. We review different works on groups yielding violations of linear rank inequalities, and discuss the classification of finite groups based on the entropic vector that they yield.…”
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Cohomology and extensions of representations of groups with normal Engel subgroups by Kissin, Edward, Shulman, Victor

“…Aiming at applications to double extensions and the theory of J-unitary group representations on indefinite metric spaces, we describe (λ, U)-cocycles when G = D n N is the semidirect product, D is an Engel group and the restrictions of λ, U to N are χ1 for some character χ on N (such pairs of representations form in a sense a base class in the variety of all pairs of representations). …”
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A critical analysis of newspaper editorial discourse on the portrayal of uprising in Libya and Syria by Afzal, Naeem, Harun, Minah

“…The theoretical framework of this study was based on van Dijk’s model of ideological square that served as a guiding principle for us to treat the editorial voices as in-group (Saudi Arabia) and out-group representations (Pakistan).We used the qualitative data analysis software package NVivo 10 to analyze the data.Findings of 12 editorial texts elucidated ‘evaluative beliefs’ of editors and their ideological constructions of authorities and protestors as social actors of the uprising. …”
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Les tableaux de fréquences 2 x 2 et leur traitement statistique by Louis Laurencelle

“…La comparaison des proportions obtenues dans deux groupes représente le modèle 1, les tailles de groupes étant prédéterminées : un test dû à Liddell et son approximation par le Khi-deux sont proposés, justifiés et validés. …”
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The Representative Potential of Interest Groups: Internal Voice in Post-Communist and Western European Countries by Joost Berkhout, Jan Beyers, Marcel Hanegraaff

“…An adequate understanding of “voice” forms the basis of “context”-embedded assessments of benchmarks such as interest group bias, interest group representational distortion, and interest group-driven policy overload. …”
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Determination of symmetry groups of 2-generator 2- groups of class two and their rationalization in molecular vibration by Aris, Nor'aini, Sarmin, Nor Haniza, Ahmad, Satapah, Masri, Rohaidah

“…From the computation, there are exactly 11 non-isomorphic families Bieberbach groups when P is cyclic group of order 2 (up to dimension 6) and their group representations, which are consistent to the polycyclic representations, are obtained. …”

An operational approach to spacetime symmetries: Lorentz transformations from quantum communication by Philipp A Höhn, Markus P Müller

“…Not only does this operational approach predict the Lorentz transformations, but it also accurately describes the behavior of relativistic Stern–Gerlach devices in the WKB approximation, and it correctly predicts that quantum systems carry Lorentz group representations of different spin. This result thus hints at a novel information-theoretic perspective on spacetime.…”
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Great Britain and the United States of America as alterity figures for Romanians in the modern epoch: Ethno-cultural images and social representations by Mihaela Mehedinți

“…Identity and alterity are thus constructed simultaneously and interdependently in accordance with group representations emerging from various sources: direct contact through travelling, mere legends or more verifiable accounts, scientific or fictional works, press articles tackling diverse topics, school textbooks, almanacs, etc. …”
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Eisenstein Series, Crystals, and Ice by Brubaker, Benjamin Brock, Bump, Daniel, Friedberg, Solomon

“…Crystal graphs encode important data associated to Lie group representations while ice models arise in the study of statistical mechanics. …”
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