Skrypnyk T. Geometric aspects of representation theory and integrable hamiltonian systems

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0400U000869

Thesis Registration Form

0400U000869.pdf

Applicant for

Specialization

  • 01.04.02 - Теоретична фізика

30-03-2000

Specialized Academic Board

Д 26.191.01

Bogolybov Institute for Theoretical Physics of NASU

Essay

The new approach for searching of integrable hamiltonian systems on orbits of finite-dimensional Lie groups is offered. The quantum integrability of mechanical systems, such as genеralized tops with symmetries, is proved. The commutativity of quantum operators which are quantum counterparts of commuting with respect to the Lie-Poisson brackets integrals of a classical Toda system on the generic co-adjoint orbits of a Borelian subgroup is proved. The higher Dolbeaut cohomology groups of the full flag manifolds are explicitly found.

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