Results 11 to 20 of about 1,413,385 (166)
Journal of High Energy Physics, 2019 We introduce an R-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra U q , t g l ^ ^ 1 $$ {U}_{q,t}\left({\widehat{\widehat{\mathfrak{gl}}}}_1\right) $$ . This R-matrix acts on pairs of 3d Young diagrams and
Hidetoshi Awata +5 more
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Machine Learning: Science and TechnologyWe provide a novel neural network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions ...
Shailesh Lal +2 more
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SciPost PhysicsA bootstrap program is presented for algebraically solving the univariate $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian.
Zhao Zhang
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The Meromorphic R-Matrix of the Yangian [PDF]
, 2021 Minor edits, one reference added. To appear in Progress in Mathematics volume for N. Reshetikhin's 60th birthday.
Gautam, Sachin +2 more
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The trigonometric $$E_8$$ R-matrix [PDF]
Letters in Mathematical Physics, 2020 An expression for the R-matrix associated to $U_q(\widehat{e_8})$ in its 249-dimensional representation is given using the diagrammatic calculus of $U_q(e_8)$ invariants.
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Chern–Simons theory and the R-matrix [PDF]
Letters in Mathematical Physics, 2021 It has been a long-standing problem how to relate Chern-Simons theory to the quantum groups. In this paper we recover the classical $r$-matrix directly from a 3-dimensional Chern-Simons theory with boundary conditions, thus creating a direct link to the quantum groups. It is known that the Jones polynomials can be constructed using an $R$-matrix.
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Peakons, r-matrix and Toda lattice [PDF]
Physica A: Statistical Mechanics and its Applications, 1996 The integrability of a family of hamiltonian systems, describing in a particular case the motionof N ``peakons" (special solutions of the so-called Camassa-Holm equation) is established in the framework of the $r$-matrix approach, starting from its Lax representation.
BRUSCHI, Mario, RAGNISCO O.
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Integral Presentations for the Universal R-Matrix
Letters in Mathematical Physics, 2000 19 pages, LaTeX 2.09 using amssym.def and amssym ...
Ding, J., Khoroshkin, S., Pakuliak, S.
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R matrix for generalized quantum group of type A [PDF]
Journal of Algebra, 2021 The generalized quantum group $\mathcal{U}(ε)$ of type $A$ is an affine analogue of quantum group associated to a general linear Lie superalgebra $\mathfrak{gl}_{M|N}$. We prove that there exists a unique $R$ matrix on tensor product of fundamental type representations of $\mathcal{U}(ε)$ for arbitrary parameter sequence $ε$ corresponding to a non ...
Kwon, Jae-Hoon, Yu, Jeongwoo
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What a Classical r-Matrix Really Is [PDF]
Journal of Nonlinear Mathematical Physics, 1999 The notion of classical $r$-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, -- where the standard definitions are shown to be deficient, -- is proposed, the notion of an ${\mathcal O}$-operator. This notion has all the natural properties one would expect form it, but lacks those which are artifacts of finite-
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