7,094 research outputs found
Think globally, compute locally
We introduce a new formulation of the so-called topological recursion, that
is defined globally on a compact Riemann surface. We prove that it is
equivalent to the generalized recursion for spectral curves with arbitrary
ramification. Using this global formulation, we also prove that the correlation
functions constructed from the recursion for curves with arbitrary ramification
can be obtained as suitable limits of correlation functions for curves with
only simple ramification. It then follows that they both satisfy the properties
that were originally proved only for curves with simple ramification.Comment: 37 pages, v2: published versio
Kac-Moody Groups and Integrability of Soliton Equations
A new approach to integrability of affine Toda field theories and closely
related to them KdV hierarchies is proposed. The flows of a hierarchy are
explicitly identified with infinitesimal action of the principal abelian
subalgebra of the nilpotent part of the corresponding affine algebra on a
homogeneous space.
This is an extended version of the paper "Generalized KdV flows and nilpotent
subgroups of affine Kac-Moody groups"; it has been accepted for publication in
Inventiones Mathematicae.Comment: 30 pages, AMSLatex; extended version accepted for publication in
Invent. Mat
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