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

Published online by Cambridge University Press:  22 January 2016

Takeshi Sasaki  and
Masaaki Yoshida
Takeshi Sasaki
Affiliation:
Department of Mathematics, Kobe University, Kobe, 657-8501, Japan
Masaaki Yoshida
Affiliation:
Department of Mathematics, Kyushu University, Fukuoka, 812-8581, Japan
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Abstract

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We find invariants for the differential systems of rank 2n in n2 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 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.

Keywords

53A5553A20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 171 , 2003 , pp. 163 - 186
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

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