Local rigidity of reducibility of analytic quasi-periodic cocycles on image Original Research Article

In this paper, we consider the reducibility problem of an analytic dd-dimensional quasi-periodic cocycle on GL(n,C)GL(n,C). We prove that, for any Diophantine vector αα and diagonal matrix CC satisfying some arithmetic conditions, if a cocycle (α,A)(α,A) can be conjugated to the constant cocycle (α,C)(α,C) by some (0,B)(0,B) with B∈L2(Td,GL(n,C))B∈L2(Td,GL(n,C)) and AA is sufficiently close to some diagonal matrix, it is analytically reducible. Moreover BB is actually analytic if it is continuous.