Lax Constraints in Semisimple Lie Groups

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    Abstract

    Instead of studying Lax equations as such, a solution Z of a Lax equation is assumed to be given. Then Z is regarded as defining a constraint on a non-autonomous linear differential equation associated with the Lax equation. In generic cases, quadrature and sometimes algebraic formulae in terms of Z are then proved for solution x of the linear differential equation, and examples are given where these formulae lead to new results in higher-order variational problems for curves in general semisimple Lie groups G, extending results previously obtained by different methods for the case where G has dimension 3. The new construction is explored in detail for G = SU(m).
    Original languageEnglish
    Pages (from-to)527-538
    JournalThe Quarterly Journal of Mathematics
    Volume57
    Issue number4
    DOIs
    Publication statusPublished - 2006

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