Lectures on meromorphic flat connections

Novikov, D.; Yakovenko, Sergeî

doi:10.1007/978-94-007-1025-2_11

Cited by 16 publications

(7 citation statements)

References 18 publications

(23 reference statements)

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“…The gauge transform corresponds to the change of a tuple of horizontal sections locally trivializing this bundle. Such interpretation allows for global and multidimensional generalizations, see Ilyashenko and Yakovenko (2008, Chapter III) and Novikov and Yakovenko (2004).…”

Section: Gauge Equivalence Of Linear Systems Equations Of the Same Typementioning

confidence: 99%

On Local Weyl Equivalence of Higher Order Fuchsian Equations

Shira

Yakovenko

2015

Arnold Math J.

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We study the local classification of higher order Fuchsian linear differential equations under various refinements of the classical notion of the "type of differential equation" introduced by Frobenius. The main source of difficulties is the fact that there is no natural group action generating this classification. We establish a number of results on higher order equations which are similar but not completely parallel to the known results on local (holomorphic and meromorphic) gauge equivalence of systems of first order equations.Keywords Fuchsian singularity · Gauge classification · Resonance · Weyl algebra 1 Local Classification of Linear Ordinary Differential Equations Systems and Higher Order EquationsThe local analytic theory of linear ordinary differential equations exists in two parallel flavours, either that of systems of several first order equations, or of scalar (higher order) equations. One can relatively easily transform one type of objects to the other, yet this transformation loses some additional structures.Let k be a differential field, called the field of coefficients. We will be interested almost exclusively in the field M = M (C 1 , 0) of meromorphic germs at the origin t = 0 on the complex line C = C 1 , the quotient field of the ring O = O(C 1 , 0) of

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Section: Gauge Equivalence Of Linear Systems Equations Of the Same Typementioning

confidence: 99%

On Local Weyl Equivalence of Higher Order Fuchsian Equations

Shira

Yakovenko

2015

Arnold Math J.

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“…The first step of the proof is the following lemma, whose statement and proof can be found in [KM97] and [Nee06]: morally it is a straight forward application of the monodromy principle for holomorphic Pfaffian systems, as described in the article [NY02].…”

Section: This Observation Concludes the Proof That Mexpmentioning

confidence: 99%

Tame Fréchet structures for affine Kac-Moody groups

Freyn

2014

Asian Journal of Mathematics

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We construct holomorphic loop groups and their associated affine Kac-Moody groups and prove that they are tame Fréchet manifolds; furthermore we study the adjoint action of these groups. These results form the functional analytic core for a theory of affine Kac-Moody symmetric spaces, that will be developed in forthcoming papers. Our construction also solves the problem of complexification of completed Kac-Moody groups: we obtain a description of complex completed Kac-Moody groups and, using this description, deduce constructions of their non-compact real forms.

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“…By the proposition, the connection on ∇ E (c,p) has regular singularities at b for all (c, p). The equality of horizontal sections in the convergent or formal setting is then well-known, see [15] for example. The second claim follows from Corollary 2.12.…”

Section: Proposition ([3] Proposition 320)mentioning

confidence: 99%