Bethe/Gauge correspondence for ABCDEFG-type 3d gauge theories by Xiang-Mao Ding, Tinglyer Zhang

“…Especially, for exceptional Lie algebras F4, G2, we give the effective superpotential and vacuum equations. …”
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Intertwining Symmetry Algebras of Quantum Superintegrable Systems by Juan A. Calzada, Javier Negro, Mariano A. del Olmo

“…We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like (su(n),so(2n)) or (su(p,q),so(2p,2q)). …”
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Geometrical/Physical Interpretation of the Conserved Quantities Corresponding to Noether Symmetries of Plane Symmetric Space-Times by Bismah Jamil, Tooba Feroze, Andrés Vargas

“…Additionally, the structure constants of the associated Lie algebras, the Riemann curvature tensors, and the energy-momentum tensors are obtained for each case. …”
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On the symmetries of singular limits of spacetimes by Eric Bergshoeff, Javier Matulich, Tomás Ortín

“…We study the isometry groups of the original spacetime metrics and of the singular metrics that arise in the limits and the corresponding symmetries of the motion of p-branes evolving in them, showing how the Killing vectors and their Lie algebras can be found in general. We illustrate our general results with several examples which include limits of anti-de Sitter spacetime in which the holographic screen is one of the singular metrics and of pp-waves.…”
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Exact Solutions of a Class of Double-Well Potentials: Algebraic Bethe Ansatz by M. Baradaran, H. Panahi

“…Also, we solve the same problems using the Lie algebraic approach of quasi-exact solvability through the sl(2) algebraization and show that the results are the same. …”
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Representation theory in complex rank, II by Etingof, Pavel I

“…Namely, we define complex rank analogs of the parabolic category O and the representation categories of real reductive Lie groups and supergroups, affine Lie algebras, and Yangians. We develop a framework and language for studying these categories, prove basic results about them, and outline a number of directions of further research. …”
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Moduli spaces of sheaves on surfaces: Hecke correspondences and representation theory by Neguţ, A

“…Its cohomology and intersection theory (as well as those of its more complicated cousins, the flag varieties) have long been studied in connection with the Lie algebras 𝔰 𝔩 n.…”
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TANGENTIAL LOCALIZATION FOR SELMER VARIETIES by Kim, M

“…This paper proposes a tangential version of the theory of Selmer varieties together with a formulation of cohomological duality in families of Lie algebras indexed by nonabelian cohomology. This theory allows one to consider deformations of cohomology classes as one moves over the Selmer variety and suggests an approach for generalizing to number fields the homotopical techniques for proving Diophantine finiteness that were developed over Q{double-struck}. …”

Second Chern-Einstein metrics on four-dimensional almost-Hermitian manifolds by Barbaro Giuseppe, Lejmi Mehdi

“…Finally, we study the second Chern-Einstein problem on unimodular almost-abelian Lie algebras, classifying those that admit a left-invariant second Chern-Einstein metric with a parallel non-zero Lee form.…”
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Line operators of gauge theories on non-spin manifolds by J.P. Ang, Konstantinos Roumpedakis, Sahand Seifnashri

“…This is used to classify all possible sets of allowed line operators — including their spins — for gauge theories with simple Lie algebras. The Lagrangian descriptions of the theories with these sets of allowed line operators are given. …”
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Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function by Schilling, Anne, Tingley, Peter

“…It has previously been shown that, at least for non-exceptional Kac-Moody Lie algebras, there is a close connection between Demazure crystals and tensor products of Kirillov-Reshetikhin crystals. …”
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On universal quantum dimensions by R.L. Mkrtchyan

“…It is based on the derivation of universal expressions for quantum dimensions (universal characters) of Cartan powers of adjoint and some other series of irreps of simple Lie algebras. These formulae also provide a proof of formulae for universal quantum dimensions for low-dimensional representations, needed in derivation of universal knot polynomials (i.e. colored Wilson averages of Chern–Simons theory on 3d sphere). …”
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Symmetric degenerations are not in general induced by type A degenerations by Magdalena Boos, Giovanni Cerulli Irelli

“…In connection with Borel orbits of 2-nilpotent matrices of classical Lie algebras, we describe an explicit example of a quiver of finite representation type for which orbit closure relations are induced in types B and C, but not in type D.…”
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Continuous-time quantum harmonic oscillator state engineering by E García Herrera, F Torres-Leal, B M Rodríguez-Lara

“…We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.…”
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Complete solution to Gaussian tensor model and its integrable properties by H. Itoyama, A. Mironov, A. Morozov

“…This is a part of the long-standing problem to define a non-Abelian lift of integrability from the fundamental to generic representation families of arbitrary Lie algebras.…”
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Two Expanding Integrable Models of the Geng-Cao Hierarchy by Xiurong Guo, Yufeng Zhang, Xuping Zhang

“…In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling) reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. …”
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THE SOCCER-BALL PROBLEM IN QUANTUM SPACE by KHRYSTYNA P. GNATENKO, VOLODYMYR M. TKACHUK

“…It is shown that this problem can be solved in a deformed space with a minimal length, in a noncommutative phase space, in a space with a Lie-algebraic noncommutativity, in a twist-deformed space-time due to the relation of parameters of corresponding algebras with mass. …”
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Logarithmic W-algebras and Argyres-Douglas theories at higher rank by Thomas Creutzig

“…Abstract Families of vertex algebras associated to nilpotent elements of simply-laced Lie algebras are constructed. These algebras are close cousins of logarithmic W-algebras of Feigin and Tipunin and they are also obtained as modifications of semiclassical limits of vertex algebras appearing in the context of S-duality for four-dimensional gauge theories. …”
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An Implementation in C of an Algorithm for Construction of Finitely Presented Lie Superalgebras by V. Gerdt, V. Kornyak

“…The purpose of this paper is to describe a C program FPLSA for investigating finitely presented Lie algebras and superalgebras. The program takes as input data a finite set of generators and relations for these elements. …”
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Maxwell superalgebras and Abelian semigroup expansion by P.K. Concha, E.K. Rodríguez

“…The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2) leads us to the Maxwell algebra M. …”
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