Invariant theory for linear differential systems modeled after the grassmannian Gr(n, 2n)

Takeshi Sasaki, Masaaki Yoshida
2003 Nagoya mathematical journal  
We find invariants for the differential systems of rank 2n in n 2 variables with n unknowns under the linear changes of the unknowns with variable coefficients. We look for a set of coefficients that determines the other coefficients, and give transformation rules under the linear changes above and coordinate changes. These can be considered as a generalization of the Schwarzian derivative, which is the invariant for second order ordinary differential equations under the change of the unknown
more » ... ge of the unknown by multiplying a non-zero function. Special treatment is done when n = 2: the conformal structure obtained through the Plücker embedding is studied, and a relation with line congruences is discussed.
doi:10.1017/s0027763000025551 fatcat:bjoafxzxa5f5xdpoa77er4ueum