Symmetric structures in the weak and strong Bruhat orders by Gao, Yibo

“…The weak and strong Bruhat orders are classical and rich combinatorial objects, with connections to Schubert calculus, Lie algebras, hyperplane arrangements, sorting networks and so on. …”
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A generalization of the alcove model and its applications by Cristian Lenart, Arthur Lubovsky

“…The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. …”
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W $$ \mathcal{W} $$ algebras are L∞ algebras by Ralph Blumenhagen, Michael Fuchs, Matthias Traube

“…Therefore, the class of well understood W $$ \mathcal{W} $$ algebras provides highly nontrivial examples of such strong homotopy Lie algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical W 3 $$ {\mathcal{W}}_3 $$ algebra.…”
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On the derived Lusztig correspondence by Gérard Laumon, Emmanuel Letellier

“…Let ${\mathfrak {g}}$ and ${\mathfrak {t}}$ be the Lie algebras of G and T. The affine variety $\mathfrak {car}={\mathfrak {t}}/\!…”
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A quantum Witt construction by Hannabuss, K

“…Given a quantum double and two suitably paired modules it is possible to construct a new quantum double, in a manner analogous to Witt's construction of simple Lie algebras. This construction generalises a standard construction of quantum groups, and also supergroups, but it also provides alternative constructions for some quantum groups, including the quantum exceptional group <em>e</em>₈. © 1998 Academic Press.…”

Symmetries and Geometries of Qubits, and Their Uses by A. R. P. Rau

“…This review brings together the Lie-algebraic/group-representation perspective of quantum physics and the geometric–algebraic one, as well as their connections to complex quaternions. …”
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Superspin chains and supersymmetric gauge theories by Nikita Nekrasov

“…Abstract We discuss the possible extensions of Bethe/gauge correspondence to quantum integrable systems based on the super-Lie algebras of A type. Along the way we propose the analogues of Nakajima quiver varieties whose cohomology and K-theory should carry the representations of the corresponding Yangian and the quantum affine algebras, respectively. …”
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Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation by Khalique Chaudry Masood, Mhlanga Isaiah Elvis

“…In this paper we study a (2+1)-dimensional coupling system with the Korteweg-de Vries equation, which is associated with non-semisimple matrix Lie algebras. Its Lax-pair and bi-Hamiltonian formulation were obtained and presented in the literature. …”
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On dimensional reduction of magical supergravity theories by Naoto Kan, Shun'ya Mizoguchi

“…This serves as a basis for the solution generating technique in this supergravity as well as allows to give the Lie algebraic characterizations to some of the parameters and functions in the original D=5 Lagrangian. …”
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Super-Laplacians and their symmetries by P. S. Howe, U. Lindström

“…The differential operators determining the symmetries give rise to algebras which can be identified in many cases with the tensor algebras of the relevant superconformal Lie algebras modulo certain ideals. They have applications to Higher Spin theories.…”
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Level two string functions and Rogers Ramanujan type identities by Arel Genish, Doron Gepner

“…The level two string functions are calculated exactly for all simply laced Lie algebras, using a ladder coset construction. These are the characters of cosets of the type G/U(1)r, where G is the algebra at level two and r is its rank. …”
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The coupling integrable couplings of the generalized coupled Burgers equation hierarchy and its Hamiltonian structure by Yuan Wei, Li Yin, Xin Long

“…Abstract In this paper, we mainly give the Lie algebras E, F and H of three kinds and their commutator, respectively. …”
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Discovering sparse representations of Lie groups with machine learning by Roy T. Forestano, Konstantin T. Matchev, Katia Matcheva, Alexander Roman, Eyup B. Unlu, Sarunas Verner

“…In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the U(n) and SU(n) families of Lie groups. …”
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Recognising Z(p)[[t]]-analytic pro-p groups by Camina, R, Du Sautoy, M

“…In the course of the proof we define a T-map, a T-uniform group and set up a category equivalence between T-uniform pro-p groups and powerful ℤ p[[t]]-Lie algebras. © 2006 Cambridge Philosophical Society.…”

On extensions of some classes of algebras by Rakhimov, Isamiddin

“…In the first part we discuss on extensions of Lie algebras and their importance in Physics. Then we deal with the extensions of some classes of algebras with one binary operation. …”
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ON GENERALIZATION OF SPECIAL FUNCTIONS RELATED TO WEYL GROUPS by Lenka Háková, Agnieszka Tereszkiewicz

“…Weyl group orbit functions are defined in the context of Weyl groups of simple Lie algebras. They are multivariable complex functions possessing remarkable properties such as (anti)invariance with respect to the corresponding Weyl group, continuous and discrete orthogonality. …”
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Generalised point vortices on a plane by Anton Galajinsky

“…In this work, integrable generalisations of the three–vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It is shown that a generalised system, which is governed by a positive definite Hamiltonian, admits a natural integrable extension by spin degrees of freedom. …”
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Clifford Algebras and Possible Kinematics by Alan S. McRae

“…We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. …”
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Reductions and conservation laws for BBM and modified BBM equations by Khorshidi Maryam, Nadjafikhah Mehdi, Jafari Hossein, Al Qurashi Maysaa

“…By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. …”
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Entropy- A Tale of Ice and Fire by Hirica Iulia-Elena, Pripoae Cristina-Liliana, Pripoae Gabriel-Teodor, Preda Vasile

“…The special values of the Tsallis parameters, highlighted by the classification of these symmetries, clearly indicate algebraic and geometric invariants which differentiate the Lie algebras involved. We compare these values with the ones previously obtained by several authors, and we try to establish connections between our theoretical families of entropies and specific entropies arising in several applications found in the literature.…”
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