Results 1 to 10 of about 53 (52)
JORDAN–KRONECKER INVARIANTS OF LIE ALGEBRA REPRESENTATIONS AND DEGREES OF INVARIANT POLYNOMIALS [PDF]
Transformation Groups, 2021 AbstractFor an arbitrary representation ρ of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan–Kronecker invariants of ρ. Among other interesting properties, these numbers provide lower bounds for degrees of polynomial invariants of ρ.
Bolsinov, A., Izosimov, A., Kozlov, I.
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Ain Shams Engineering Journal, 2021 The regularized and the modified regularized long wave (RLW and MRLW) equations are solved numerically by the Bernstein polynomials in both the space and time directions based on Kronecker product.
D.A. Hammad
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JORDAN–KRONECKER INVARIANTS OF FINITE-DIMENSIONAL LIE ALGEBRAS [PDF]
Transformation Groups, 2015 For any finite-dimensional Lie algebra we introduce the notion of Jordan-Kronecker invariants, study their properties and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable systems on Lie algebras and are closely related to Mischenko-Fomenko's argument shift method.
Bolsinov, A. V., Zhang, P.
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Fundamental Invariants of Tensors, Latin Hypercubes, and Rectangular Kronecker Coefficients
International Mathematics Research Notices, 2022 Abstract We study polynomial SL-invariants of tensors, mainly focusing on fundamental invariants that are of smallest degrees. In particular, we prove that certain 3-dimensional analogue of the Alon–Tarsi conjecture on Latin cubes considered previously by Bürgisser and Ikenmeyer implies positivity of (generalized) Kronecker coefficients ...
Amanov, Alimzhan, Yeliussizov, Damir
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Ramanujan’s class invariants, Kronecker’s limit formula, and modular equations [PDF]
Transactions of the American Mathematical Society, 1997 In his notebooks, Ramanujan gave the values of over 100 class invariants which he had calculated. Many had been previously calculated by Heinrich Weber, but approximately half of them had not been heretofore determined. G. N. Watson wrote several papers devoted to the calculation of class invariants, but his methods were not entirely rigorous. Up until
Berndt, Bruce C. +2 more
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Invariant operators, orthogonal bases and correlators in general tensor models
Nuclear Physics B, 2018 We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry Gd=U(N1)⊗⋯⊗U(Nd).
Pablo Diaz, Soo-Jong Rey
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Cluster algebras, invariant theory, and Kronecker coefficients I [PDF]
Advances in Mathematics, 2017 40 pages, 20 figures, comments are ...
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Ramanujan's class invariants, Kronecker's limit formula and modular equations (III) [PDF]
Acta Arithmetica, 1997 [For parts I and II, see \textit{B. C. Berndt}, \textit{H. H. Chan}, and \textit{L.-C. Zhang}, Trans. Am. Math. Soc. 349, 2125-2173 (1997; Zbl 0885.11058) and \textit{L.-C. Zhang}, Prog. Math. 139, 817-838 (1996; Zbl 0877.11062).] The author continues previous work by proving the five remaining cases of Ramanujan's class invariants.
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Formulas for Kronecker invariants using a representation theoretical approach
Linear Algebra and its Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Szántó, Csaba, Horváth, Alexandru
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Realization of Jordan-Kronecker invariants by Lie algebras
, 2023 We study what Jordan-Kronecker invariants of Lie algebras, introduced by A. V. Bolsinov and P. Zhang, are possible. We completely solve this problem in the Jordan and the Kronecker cases. We prove that any JK invariants that contain the Kronecker $3 \times 3$ block or several Kronecker $1 \times 1$ blocks are possible.
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