Modern definitions and properties of special orbits-functions of simple Lie algebras are systematized. Models of carbon modifications related to simple Lie algebras and Coxeter groups are proposed.
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I. A. Dynnikov and S. P. Novikov, “Geometry of the triangle equation on two-manifolds,” Mosc. Math. J., 3, 419–438 (2003); https://doi.org/10.17323/1609-4514-2003-3-2-419-438.
N. Bourbaki, Lie Groups and Lie Algebras, Chaps. 3–6, Springer, Berlin (1989).
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Univ. Press, Cambridge (1990).
A. Klimyk and J. Patera, “Orbit functions,” SIGMA, 2, 006 (2006); https://doi.org/10.3842/SIGMA.2006.006.
A. Klimyk and J. Patera, “Antisymmetric orbit functions,” SIGMA, 3, 023 (2007); https://doi.org/10.3842/SIGMA.2007.023.
R. V. Moody, L. Motlochová, and J. Patera, “Gaussian cubature arising from hybrid characters of simple Lie groups,” J. Fourier Anal. Appl., 20, 1257–1290 (2014); https://doi.org/10.1007/s00041-014-9355-0.
M. Szajewska and A. Tereszkiewicz, “Multidimensional hybrid boundary value problem,” Acta Polytech., 58, No. 6, 402–413 (2018). https://doi.org/10.14311/AP.2018.58.0402.
J. Hrivnák and L. Motlochová, “Dual-root lattice discretization of Weyl orbit functions,” J. Fourier Anal. Appl., 25, 2521–2569 (2019); https://doi.org/10.1007/s00041-019-09673-1.
M. Nesterenko and J. Patera, “Three-dimensional C-, S-, and E-transforms,” J. Phys. A, 41, 475205 (2008); https://doi.org/10.1088/1751-8113/41/47/475205.
M. Nesterenko, J. Patera, M. Szajewska, and A. Tereszkiewicz, “Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials,” J. Phys. A, 43, 495207 (2010); https://doi.org/10.1088/1751-8113/43/49/495207.
M. Nesterenko, J. Patera, and A. Tereszkiewicz, “Orthogonal polynomials of compact simple Lie groups,” Int. J. Math. Math. Sci., 2011, 969424 (2011); https://doi.org/10.1155/2011/969424.
M. Bodner, E. Bourret, J. Patera, and M. Szajewska, “Icosahedral symmetry breaking: C60 to C78, C96 and to related nanotubes,” Acta Cryst. A, 70, 650–655 (2014); https://doi.org/10.1107/S2053273314017215.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 3, pp. 351–359, March, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i3.7130.
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Nesterenko, M.O. Special Exponential Functions on Lattices of Simple Lie Algebras and the Allotropic Modifications of Carbon. Ukr Math J 74, 395–404 (2022). https://doi.org/10.1007/s11253-022-02071-9
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DOI: https://doi.org/10.1007/s11253-022-02071-9