

International conference "Geometrical Methods in Mathematical Physics"
December 16, 2011 16:45–17:30, Moscow, Lomonosov Moscow State University






Cartan matrices and integrable lattice Toda field equations
I. T. Habibullin^{} ^{} Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa

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Abstract:
Differentialdifference integrable exponential type systems are studied
corresponding to the Cartan matrices of semisimple or affine Lie algebras.
For the systems corresponding to the algebras $A_{2},B_{2},C_{2},G_{2}$ the
complete sets of integrals in both directions are found.
For the simple Lie algebras of the classical series $A_{N},B_{N},C_{N}$ and
affine algebras of series $D_{N}^{(2)}$ the corresponding systems are
supplied with the Lax representation.
References.
[1] Ismagil Habibullin, Kostyantyn Zheltukhin and Marina Yangubaeva, Cartan
matrices
and integrable lattice Toda field equations, J. Phys. A: Math. Theor. 44
(2011) 465202
(20pp).
[2] Ismagil Habibullin, Rustem N. Garifullin, Affine Lie algebras and
integrable Toda field
equations on discrete spacetime, arXiv:1109.1689 (2011).
Materials:
gmmp2011_ihabibullin.pdf (294.5 Kb)
Language: English

