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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
Materials:
Adobe PDF 294.5 Kb

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Abstract: Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple 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 space-time, arXiv:1109.1689 (2011).

Materials: gmmp2011_ihabibullin.pdf (294.5 Kb)

Language: English

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