Rigid local systems and quantum cohomology of the Grassmannian
-- Prakash Belkale, December 3, 2004

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A rigid local system on a punctured Riemann sphere is a
representation of the fundamental group into GL(n,C) which
has no deformations (keeping the local monodromies fixed). It
is known (Simpson, Katz) that every rigid local system has
monodromy in a U(p,q).  In the talk we will discuss the case
when the monodromy is unitary. We will show how non-vanishing
Gromov-Witten numbers produce unitary local systems and the
relation between rigidity and the property GW-number = 1.  The
place of rigid local systems in the classification of unitary
local syetems will also be considered.