TITLE:
Equivalence of Paths under the Action of the Real Representation of Sp(n)
AUTHORS:
Muminov K. Khodyrovich, Juraboyev S. Solyjonovich
KEYWORDS:
Real Representation, Differential Invariant, Differential Generators, Path in a Finite-Dimensional Space
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.5,
May
31,
2022
ABSTRACT: In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.