Special exponential functions on lattices of simple Lie groups and allotropic modifications of carbon

  • M. O. Nesterenko Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv
Keywords: orbit function, root system, hexagonal tiling, fullerene

Abstract

UDC 517.9

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.

 

References

I. A. Dynnikov, 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, Chapters 3 – 6, Springer-Verlag, Berlin,-New York (1989).

J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge University Press, Cambridge (1990).

A. Klimyk, J. Patera, Orbit functions, SIGMA, 2, 006 (2006), 60 pp.; https://doi.org/10.3842/SIGMA.2006.006

A. Klimyk, J. Patera, Antisymmetric orbit functions, SIGMA, 3, 023 (2007), 83 pp.; https://doi.org/10.3842/SIGMA.2007.023

R. V. Moody, L. Motlochova, 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, A. Tereszkiewicz, Multidimensional hybrid boundary value problem, Acta Polytechnica 58, № 6, 402 – 413 (2018), https://doi.org/10.14311/AP.2018.58.0402

J. Hrivnák, L. Motlochova, 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, J. Patera, Three-dimensional $C$-, $S$- and E-transforms, J. Phys. A, 41, 475205 (2008), 31 pp.; https://doi.org/10.1088/1751-8113/41/47/475205

M. Nesterenko, J. Patera, M. Szajewska, A. Tereszkiewicz, Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials, J. Phys. A, 43, 495207 (2010), 27 pp.; https://doi.org/10.1088/1751-8113/43/49/495207

M. Nesterenko, J. Patera, A. Tereszkiewicz, Orthogonal polynomials of compact simple Lie groups, Int. J. Math. Math. Sci., 2011, 969424 (2011), 23 pp.; https://doi.org/10.1155/2011/969424.

M. Bodner, E. Bourret, J. Patera, 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.

Published
26.04.2022
How to Cite
NesterenkoM. O. “Special Exponential Functions on Lattices of Simple Lie Groups and Allotropic Modifications of Carbon”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 3, Apr. 2022, pp. 351-9, doi:10.37863/umzh.v74i3.7130.
Section
Research articles