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Regular coordinates and reduction of deformation equations for Fuchsian systems

Yoshishige Haraoka (2012)

Banach Center Publications

For a Fuchsian system d Y / d x = ( j = p ( A j ) / ( x - t j ) ) Y , (F) t , t , . . . , t p being distinct points in ℂ and A , A , . . . , A p M ( n × n ; ) , the number α of accessory parameters is determined by the spectral types s ( A ) , s ( A ) , . . . , s ( A p ) , where A = - j = 1 p A j . We call the set z = ( z , z , . . . , z α ) of α parameters a regular coordinate if all entries of the A j are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues of the matrices...

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