Invariant theory for linear differential systems modeled after the grassmannian Gr(n, 2n)
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Rank 2
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AbstractWe 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.
2019 ◽
Vol 74
(3)
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pp. 121-126
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2020 ◽
Vol 7
(1)
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pp. 237-248
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2012 ◽
Vol 47
(2)
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pp. 192-213
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Keyword(s):
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