Upper triangularity for unipotent representations by Mason-Brown, L

“…These representations are `attached' (in a certain mysterious sense) to the nilpotent orbits of G on the dual space of its Lie algebra. Inside this finite set is a still smaller set, consisting of the unipotent representations attached to non-induced nilpotent orbits. …”

Hidden symmetries, the Bianchi classification and geodesics of the quantum geometric ground-state manifolds by Diego Liska, Vladimir Gritsev

“…We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. …”
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Harmonic Analysis in One-Parameter Metabelian Nilmanifolds by Amira Ghorbel

“…Let G be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. …”
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Exact self-duality in a modified Skyrme model by L.A. Ferreira

“…The action of such a theory possesses the usual quadratic and quartic terms in field derivatives, but the couplings of the components of the Maurer-Cartan form of the Skyrme model is made by a non-constant symmetric matrix, instead of the usual Killing form of the SU(2) Lie algebra. The introduction of such a matrix make the self-duality equations conformally invariant in three space dimensions, even though it may break the global internal symmetries of the original Skyrme model. …”
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On reducing and finding solutions of nonlinear evolutionary equations via generalized symmetry of ordinary differential equations by Ivan Tsyfra, Wojciech Rzeszut

“…We prove a theorem relating the property of invariance of a found solution to the dimension of the Lie algebra admitted by the corresponding equation. …”
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Gauge theory on twist-noncommutative spaces by Tim Meier, Stijn J. van Tongeren

“…This includes particular Lie-algebraic and quadratic noncommutative structures. …”
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More on pure gravity with a negative cosmological constant by Lior Benizri, Jan Troost

“…Abstract We identify an ambiguity in the Chern-Simons formulation of three-dimensional gravity with negative cosmological constant that originates in an outer automorphism of the Lie algebra sl $$ \mathfrak{sl} $$ (2, ℝ). It has important consequences for the stability of the theory in a space-time with boundary. …”
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The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid by Jonas T. Hartwig

“…Using the language of 𝔥-Hopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, ℱell(GL(n)), from the elliptic solution of the quantum dynamical Yang-Baxter equation with spectral parameter associated to the Lie algebra 𝔰𝔩n. We apply the generalized FRST construction and obtain an 𝔥-bialgebroid ℱell(M(n)). …”
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Non-split singularities and conifold transitions in F-theory by R. Kuramochi, S. Mizoguchi, T. Tani

“…In the latter case, the gauge symmetry is reduced to a non-simply-laced Lie algebra due to monodromy. We show that this split/non-split transition is, except for a special class of models, a conifold transition from the resolved to the deformed side, associated with the conifold singularities emerging where the codimension-one singularity is enhanced to D 2k+2 (k ≥ 1) or E 7. …”
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Mathematical Details on a Cancer Resistance Model by James M. Greene, Cynthia Sanchez-Tapia, Eduardo D. Sontag, Eduardo D. Sontag

“…The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebraic techniques. A structural identifiability analysis is also presented, demonstrating that patient-specific parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy. …”
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Deformed su(1,1) Algebra as a Model for Quantum Oscillators by Elchin I. Jafarov, Neli I. Stoilova, Joris Van der Jeugt

“…The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su}(1,1) can be extended to representations of this deformed algebra su(1,1)_gamma. …”
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Exploring exceptional Drinfeld geometries by Chris D. A. Blair, Daniel C. Thompson, Sofia Zhidkova

“…This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. …”
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Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations by Hitoshi Konno

“…For any affine Lie algebra ${mathfrak g}$, we show that any finite dimensional representation of the universal dynamical $R$ matrix ${cal R}(lambda)$ of the elliptic quantum group ${cal B}_{q,lambda}({mathfrak g})$ coincides with a corresponding connection matrix for the solutions of the $q$-KZ equation associated with $U_q({mathfrak g})$. …”
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Path-integral quantization of tensionless (super) string by Bin Chen, Zezhou Hu, Zhe-fei Yu, Yu-fan Zheng

“…Taking the BMS bc and βγ ghosts as new types of BMS free field theories, we find that their enhanced underlying symmetries are generated by BMS-Kac-Moody algebras, with the Kac-Moody subalgebras being built from a three-dimensional non-abelian and non-semi-simple Lie algebra.…”
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On the integrable gravity coupled to fermions by Vladimir A. Belinski

“…In this way the integrability technique for simple (N=1) supergravity in two space-time dimensions coupled to the matter fields taking values in the Lie algebra of E8(+8) group is developed. This theory contains matter living only in one Weyl representation of SO(16) and represents the reduction to two dimensions of the three-dimensional simple supergravity constructed in [1]. …”
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Integrable boundary conditions in the antiferromagnetic Potts model by Niall F. Robertson, Michal Pawelkiewicz, Jesper Lykke Jacobsen, Hubert Saleur

“…Abstract We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine D 2 2 $$ {D}_2^2 $$ Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. …”
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A Common Structure in PBW Bases of the Nilpotent Subalgebra of U_q(g) by Atsuo Kuniba, Masato Okado, Yasuhiko Yamada

“…For a finite-dimensional simple Lie algebra $mathfrak{g}$, let $U^+_q(mathfrak{g})$ be the positive part of the quantized universal enveloping algebra, and $A_q(mathfrak{g})$ be the quantized algebra of functions. …”
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Notes on higher-derivative conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string by Yuri Makeenko

“…I show that the conformal transformations generated by the nonprimary energy-momentum tensor form a Lie algebra with a central extension which in the path-integral formalism gives a logarithmically divergent contribution to the central charge. …”
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Breaking and permanent waves for the periodic μ-Degasperis–Procesi equation with linear dispersion by Fei Guo

“…Abstract Considered herein is the periodic μ-Degasperis–Procesi equation, which is an evolution equation on the space of tensor densities over the Lie algebra of smooth vector fields. First two conditions on the initial data that lead to breaking waves in finite time are formulated. …”
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Order Filter Model for Minuscule Plücker Relations by David C Lax

“…To do this we combinatorially model the Plücker coordinates based on Wild-berger’s construction of minuscule Lie algebra representations; it uses the colored partially ordered sets known asminuscule posets. …”
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